anonymous
  • anonymous
What is the f'(x) of f(X)=sin^3x
Calculus1
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Have you attempted this one yet ?
anonymous
  • anonymous
yeah
anonymous
  • anonymous
\[f(x) = \sin ^{3}(x)\] Did I write this down correctly? If so, try substitution. For example, let u = sin(x) and then take the derivative of u^3

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anonymous
  • anonymous
I got f'(X) is 9x^2cosx^2
anonymous
  • anonymous
that is 3u^2
anonymous
  • anonymous
3u^2 du/dx, yes. Now what is du/dx if u = sin x?
anonymous
  • anonymous
In other words, what is u' if u = sin x
anonymous
  • anonymous
cosx^2
anonymous
  • anonymous
What is the derivative of sin(x) ?
anonymous
  • anonymous
COS
anonymous
  • anonymous
Great, so du/dx = cos x So we have 3u^2 * cos x Substitute u = sin(x) back in and what do we end up with ?
anonymous
  • anonymous
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