What I grasped from the 9 minute video on derivatives is that solving for derivatives is solving for the slope of a function that may not have a constant slope, like a linear function will. To solve for the derivative, you take two points along the function. Let's say the first point is (a, f(a)) and the second is (a+h, f(a=h)). You use the y-y/x-x formula to solve for the slope of this approximated line, called the secant line. The derivative is then the limit of this equation! The actual definition of a derivative is the limit of f(a+h) - f(a)/(a=h) - a as h approaches 0.
I think it's cool that everything is coming full circle and seems to be linked in calculus: algebra, limits, trig, etc. Now if only I could wrap my brain around WHY this makes sense. That's the tough part. Practice makes perfect!
I thought it was interesting to see how slopes now become derivatives and thus have a higher importance in math. The video was a good introduction and I like having these lessons as resources.
I also agree with everything Mikayla said; I think she just about sums it all up.
I think that this video was a little bit jumbled (with all of the drawing and color choice issues...) but I understood it by the end when he said that the derivative is found by calculating the slope of a certain point on a curve. He also said that this is the limit of the function. (?) I agree with Mikayla, the tough part is just sort of wrapping my brain around these ideas and how it all connects.
Overall, I thought the video was full of good information and I liked being able to pause and rewind when needed to jot down a few notes. I had no prior background on derivatives before, and this video taught me what it was: the slope of a curve at an exact point. I learned that the definition of a derivative was "the limit of f(a+h) - f(a) / h as h approaches 0." Like Mikayla said, it was interesting to hear many concepts that we've learned in prior classes (trig, limits, etc) be combined all in one. I thought this video was a great introduction to derivatives. :)
I think this video was awesome, it explained alot. To solve for a derivative, is to basically get the slope, for example if you had a curve (x^2), you would mark two points on it and find the slope of those two points using the x2-x1/y2-y1 method. You would then mark the x axis point as h and the y axis point as f(h), and do the same method for the other point marking it as c at the x axis and f(c) at the y axis.
The video provided a good introduction to derivatives and was helpful in explaining the general process of finding the slope of a point on a curve using tangent lines and limits.
This video helped me to understand what the derivatives video is based off of and how to apply it. I now see that the derivatives formula is based off of the slope formula and this helped me to understand how it is used. After watching this video I now feel like I have a more clear understanding of how to apply and use derivatives.
I thought the video was helpful and it summed up all the previous things we learned about slope and added some new informations which was a little confusing. The slope is the same across the whole line and you can find the slope of the line by any two points. Slope and derivates are the same thing and the equation is f(a+h) - f(a)/(a=h) as it gets closer to zero. I think it was a good introduction and it gives more insight to what we are doing in class. However, as the ideo went on I got a little confused on finding it. -Holly
I thought the video had a great introduction for derivatives. However, I found it very confusing! I think it may take me a while to completely understand derivative, but the other derivative videos from Khan Academy will help. The most important thing that I learned from the video is that a derivative is "the slope of a curve at an exact point."
When learning about derivatives, this video was a helpful introduction. However, I thought it was a bit too visual, focusing on how the graphs would look rather than how to do the algebra to find the answer to a possible question. If I understood how to find a derivative, I think the video would have helped me visualize better why I was doing the algebra
This video i found really helpful because he explained in depth about finding the derivative of a curve. he picked to pints using the delta y over the delta x method.
I felt this was a very helpful video because it Mr. Khan explained the process of finding derivatives while actually doing a problem out. Derivatives are the same as slope, except for a curve. You can find the derivative of a curve with tangents.
This video of derivatives helped me understand I did not fully grasp from the book and class. His use of graphs allowed me to visually learn about derivatives. Understanding how to calculate the slope of a curve is a vital part of calculus.
The video helped me to understand how derivatives are found within graphs and the specific point on the curve of the line to help me find the slope at any point on the entire function.
What this video helped me is for understand the derivatives, and what is "h", and how to resolve a derivative. Also, it helps me to understand why is the lim f(x) when h->0
The video really helped me understand the basics of derivatives in the way that it was so simply put and clear, especially with the use of the drawings as he went step by step. I definitely think the video's a good resource and will be really helpful when it comes time to review for midterms and finals.
I thought this video was very helpful in restating everything I knew and really making it click with me. Although I already understood how to solve for them, the 9 min video allowed me to make sure I understood WHY you solve the way you do. I also like how it showed how limits fit in with derivatives and how they're helpful. Also, being able to pause and re-watch things was very helpful when trying to understand what was being explained!
I found the speaker in this video very helpful. He speaks in a cool calm and collected manner that makes learning a breeze. I found it interesting to find out where the formula comes from. Before this video I did not know the reason why the formula works.
I thoroughly enjoyed the Kahn video on derivatives. I'm much more of a visual learner and I loved how the video had diagrams and did the process with you. Also Mr. Kahn made it amusing and enjoyable to learn about the tough mathematical process and before I knew it the nine minutes were over.
Watching this video really cleared up a lot of the confusion that I had over derivatives. Originally I missed the lesson on derivatives, but after watching this they make a lot more sense to me. Whereas before, the entire equation for the derivative never really made much sense to me beyond what was explained by a friend, now I understand how it is basically the same as the regular formula for slope, change in y over change in x.
Also, I fully understand what a tangent and secant line are now.
I really liked the khan academy video of derivatives. It helped me to better understand the meaning of derivatives and how to solve them. I also liked how it showed the connection with the slope formula. Not only did it help me to understanding solving but its connection with limits and why we are taught them together.
What I grasped from the 9 minute video on derivatives is that solving for derivatives is solving for the slope of a function that may not have a constant slope, like a linear function will. To solve for the derivative, you take two points along the function. Let's say the first point is (a, f(a)) and the second is (a+h, f(a=h)). You use the y-y/x-x formula to solve for the slope of this approximated line, called the secant line. The derivative is then the limit of this equation! The actual definition of a derivative is the limit of f(a+h) - f(a)/(a=h) - a as h approaches 0.
ReplyDeleteI think it's cool that everything is coming full circle and seems to be linked in calculus: algebra, limits, trig, etc. Now if only I could wrap my brain around WHY this makes sense. That's the tough part. Practice makes perfect!
- Mikayla
I thought it was interesting to see how slopes now become derivatives and thus have a higher importance in math. The video was a good introduction and I like having these lessons as resources.
ReplyDeleteI also agree with everything Mikayla said; I think she just about sums it all up.
This comment has been removed by the author.
ReplyDeleteI think that this video was a little bit jumbled (with all of the drawing and color choice issues...) but I understood it by the end when he said that the derivative is found by calculating the slope of a certain point on a curve. He also said that this is the limit of the function. (?) I agree with Mikayla, the tough part is just sort of wrapping my brain around these ideas and how it all connects.
ReplyDeleteOverall, I thought the video was full of good information and I liked being able to pause and rewind when needed to jot down a few notes. I had no prior background on derivatives before, and this video taught me what it was: the slope of a curve at an exact point. I learned that the definition of a derivative was "the limit of f(a+h) - f(a) / h as h approaches 0." Like Mikayla said, it was interesting to hear many concepts that we've learned in prior classes (trig, limits, etc) be combined all in one. I thought this video was a great introduction to derivatives. :)
ReplyDeleteI think this video was awesome, it explained alot. To solve for a derivative, is to basically get the slope, for example if you had a curve (x^2), you would mark two points on it and find the slope of those two points using the x2-x1/y2-y1 method. You would then mark the x axis point as h and the y axis point as f(h), and do the same method for the other point marking it as c at the x axis and f(c) at the y axis.
ReplyDeleteThe video provided a good introduction to derivatives and was helpful in explaining the general process of finding the slope of a point on a curve using tangent lines and limits.
ReplyDeleteThis video helped me to understand what the derivatives video is based off of and how to apply it. I now see that the derivatives formula is based off of the slope formula and this helped me to understand how it is used. After watching this video I now feel like I have a more clear understanding of how to apply and use derivatives.
ReplyDeleteI posted my comment ms. lebzelter. did you see it? did ya?
ReplyDeleteI thought the video was helpful and it summed up all the previous things we learned about slope and added some new informations which was a little confusing. The slope is the same across the whole line and you can find the slope of the line by any two points. Slope and derivates are the same thing and the equation is f(a+h) - f(a)/(a=h) as it gets closer to zero. I think it was a good introduction and it gives more insight to what we are doing in class. However, as the ideo went on I got a little confused on finding it.
ReplyDelete-Holly
I thought the video had a great introduction for derivatives. However, I found it very confusing! I think it may take me a while to completely understand derivative, but the other derivative videos from Khan Academy will help. The most important thing that I learned from the video is that a derivative is "the slope of a curve at an exact point."
ReplyDeleteWhen learning about derivatives, this video was a helpful introduction. However, I thought it was a bit too visual, focusing on how the graphs would look rather than how to do the algebra to find the answer to a possible question. If I understood how to find a derivative, I think the video would have helped me visualize better why I was doing the algebra
ReplyDeleteThe video explained about finding the derivative of a curve
ReplyDeleteThis video i found really helpful because he explained in depth about finding the derivative of a curve. he picked to pints using the delta y over the delta x method.
ReplyDeleteI thought this was very helpful in understanding the derivatives. It helped how to find the derivative of a curve and using the slope formula.
ReplyDeleteI felt this was a very helpful video because it Mr. Khan explained the process of finding derivatives while actually doing a problem out. Derivatives are the same as slope, except for a curve. You can find the derivative of a curve with tangents.
ReplyDeleteThis video of derivatives helped me understand I did not fully grasp from the book and class. His use of graphs allowed me to visually learn about derivatives. Understanding how to calculate the slope of a curve is a vital part of calculus.
ReplyDeleteThe video helped me to understand how derivatives are found within graphs and the specific point on the curve of the line to help me find the slope at any point on the entire function.
ReplyDeleteWhat this video helped me is for understand the derivatives, and what is "h", and how to resolve a derivative.
ReplyDeleteAlso, it helps me to understand why is the lim f(x) when h->0
The video really helped me understand the basics of derivatives in the way that it was so simply put and clear, especially with the use of the drawings as he went step by step. I definitely think the video's a good resource and will be really helpful when it comes time to review for midterms and finals.
ReplyDeleteI thought this video was very helpful in restating everything I knew and really making it click with me. Although I already understood how to solve for them, the 9 min video allowed me to make sure I understood WHY you solve the way you do. I also like how it showed how limits fit in with derivatives and how they're helpful. Also, being able to pause and re-watch things was very helpful when trying to understand what was being explained!
ReplyDeleteI found the speaker in this video very helpful. He speaks in a cool calm and collected manner that makes learning a breeze. I found it interesting to find out where the formula comes from. Before this video I did not know the reason why the formula works.
ReplyDeleteI thoroughly enjoyed the Kahn video on derivatives. I'm much more of a visual learner and I loved how the video had diagrams and did the process with you. Also Mr. Kahn made it amusing and enjoyable to learn about the tough mathematical process and before I knew it the nine minutes were over.
ReplyDeleteWatching this video really cleared up a lot of the confusion that I had over derivatives. Originally I missed the lesson on derivatives, but after watching this they make a lot more sense to me. Whereas before, the entire equation for the derivative never really made much sense to me beyond what was explained by a friend, now I understand how it is basically the same as the regular formula for slope, change in y over change in x.
ReplyDeleteAlso, I fully understand what a tangent and secant line are now.
I really liked the khan academy video of derivatives. It helped me to better understand the meaning of derivatives and how to solve them. I also liked how it showed the connection with the slope formula. Not only did it help me to understanding solving but its connection with limits and why we are taught them together.
ReplyDelete