anonymous
  • anonymous
Chain rule with e^(x^2)
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
e(x^2)*2x
anonymous
  • anonymous
how did you do it :) ?
anonymous
  • anonymous
derivative of outside times derivative of inside

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anonymous
  • anonymous
f'(g(x)*g'(x)
anonymous
  • anonymous
i just dont get it ... what is the outside and what the inside part here ... and how do i figure that out?
anonymous
  • 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
  • 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
  • anonymous
so it would actually be written "(e^x)^2" ? ... which would make "e^x" the inner function?
anonymous
  • anonymous
the (x^2) would be the innermost function.
anonymous
  • anonymous
You have to deal with both e^x^2 function and the x^2 function.
anonymous
  • anonymous
And according to the chain rule, you multiply both derivatives together. Is this clear?
anonymous
  • anonymous
x^2 is the inner function but it doesnt matter
anonymous
  • 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
  • anonymous
you can do derivative of inside times outside or vice versa. Its more on how you define f and g
anonymous
  • 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
  • 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
  • anonymous
yea i got it, we arent aloud to use graphing calculators
anonymous
  • anonymous
its 0 and 2pi
anonymous
  • anonymous
oopps, I meant -2sin(θ) + sin(2θ) = 0
anonymous
  • anonymous
Oh nice. Good.
anonymous
  • anonymous
thanks i gotta get ready, please fan me if i helped
anonymous
  • anonymous
sorry ... gotta ask once again. how do you know "x^2" is the inner function here?
anonymous
  • anonymous
its e raised to a parenthesis e^x is the first function and x=x^2
anonymous
  • anonymous
you have to learn to distinguish between your inside and outside functions
anonymous
  • anonymous
It is the innermost function because it is the one closest to x. You cannot not differentiate further.
anonymous
  • anonymous
i really gotta get ready for class so see if IPARKE can help you
anonymous
  • anonymous
thank you thank you thank you ... big help :)

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