Question

Using Chain Rule: Write the composite function in the form f(g(x)). [Identify the inner function u=g(x) and the outer function y=f(u).] Then find the derivative dy/dx for (1-x^2)^10

Answer 1

Hey there Jenny! :)
You so short! Grow some legs!

jk jk, but anyway, ok ok we having some trouble with composition?

Answer 2

\[\Large\rm \color{royalblue}{(}\color{orangered}{1-x^2}\color{royalblue}{)^2}\]Here is one way we can break it up...

Answer 3

\[\Large\rm \color{orangered}{u=g(x)=1-x^2}\]

Answer 4

\[\Large\rm \color{royalblue}{f(}x\color{royalblue}{)=(}x\color{royalblue}{)^2}\]\[\Large\rm \color{royalblue}{f(}\color{orangered}{u}\color{royalblue}{)=(}\color{orangered}{u}\color{royalblue}{)^2}\]\[\Large\rm \color{royalblue}{f(}\color{orangered}{u}\color{royalblue}{)=}\color{royalblue}{(}\color{orangered}{1-x^2}\color{royalblue}{)^2}\]

Answer 5

Mmmm what'd ya think jen jen? :o

Answer 6

So I'm calling the outer function (stuff)^2

and the inner function is the stuff

Answer 7

Thank you so much because that was the part where I was a lost at.

Answer 8

cool c:

Try to get a lot of practice with the chain rule,
it is by far the hardest of the shortcut rules to master.

Answer 9

I will definitely try. I'm not dong so hot in AP Calc and it's really stressing me out. Thank you!

Answer 10

Oh oh you still need to find the derivative of this function.
Any trouble with that?

Answer 11

The first step in that would look like: f'(x)= 10(1-x^2)^9 times the derivative of 1-x^2 correct?

Answer 12

Mmmm yes very nice!
The inner function stays the same, as you have it written,
power rule,
then bam, you'll make a copy of the inside and multiply on the outside by the derivative of that.

Answer 13

Awesome thank you!

Answer 14

Then you would end up with f'(x)= 10(1-x^2)^9 multiplied by 2x?