Chain rule with e^(x^2)

- anonymous

Chain rule with e^(x^2)

- katieb

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- anonymous

e(x^2)*2x

- anonymous

how did you do it :) ?

- anonymous

derivative of outside times derivative of inside

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## More answers

- anonymous

f'(g(x)*g'(x)

- anonymous

i just dont get it ... what is the outside and what the inside part here ... and how do i figure that out?

- anonymous

e^x's derivative is just e^x so e^(x^2)'s derivative is just e^(x^2) then you multiply that by the derivative of x^2 which is 2x

- anonymous

usually just consider the numbers in the parenthesis as the inside when looking at this function (x+2)^3's derivative would be 3(x+2)^2*1

- anonymous

so it would actually be written "(e^x)^2" ? ... which would make "e^x" the inner function?

- anonymous

the (x^2) would be the innermost function.

- anonymous

You have to deal with both e^x^2 function and the x^2 function.

- anonymous

And according to the chain rule, you multiply both derivatives together. Is this clear?

- anonymous

x^2 is the inner function but it doesnt matter

- anonymous

now it is ... thank you soooo much. i really really do appreciate it. i have been pondering over this for over an hour by now.

- anonymous

you can do derivative of inside times outside or vice versa. Its more on how you define f and g

- anonymous

try to see if you can distinguish in many problems the outside and inside then you are all set if you can do that because derivatives are easy from there if you know the rules and how to apply them

- anonymous

Haha, Saif, without a graphing calc, your problem is difficult. Off topic, I've narrowed f'(θ) to -sin(θ) + sin(2θ) = 0 if you can take it from there.

- anonymous

yea i got it, we arent aloud to use graphing calculators

- anonymous

its 0 and 2pi

- anonymous

oopps, I meant -2sin(θ) + sin(2θ) = 0

- anonymous

Oh nice. Good.

- anonymous

thanks i gotta get ready, please fan me if i helped

- anonymous

sorry ... gotta ask once again. how do you know "x^2" is the inner function here?

- anonymous

its e raised to a parenthesis e^x is the first function and x=x^2

- anonymous

you have to learn to distinguish between your inside and outside functions

- anonymous

It is the innermost function because it is the one closest to x. You cannot not differentiate further.

- anonymous

i really gotta get ready for class so see if IPARKE can help you

- anonymous

thank you thank you thank you ... big help :)

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