## Alexalayne 2 years ago What is the f'(x) of f(X)=sin^3x

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1. LogicalApple

Have you attempted this one yet ?

2. Alexalayne

yeah

3. LogicalApple

$f(x) = \sin ^{3}(x)$ Did I write this down correctly? If so, try substitution. For example, let u = sin(x) and then take the derivative of u^3

4. Alexalayne

I got f'(X) is 9x^2cosx^2

5. Alexalayne

that is 3u^2

6. LogicalApple

3u^2 du/dx, yes. Now what is du/dx if u = sin x?

7. LogicalApple

In other words, what is u' if u = sin x

8. Alexalayne

cosx^2

9. LogicalApple

What is the derivative of sin(x) ?

10. Alexalayne

COS

11. LogicalApple

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 ?

12. LogicalApple

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