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Alexalayne

  • 3 years ago

What is the f'(x) of f(X)=sin^3x

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  1. LogicalApple
    • 3 years ago
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    Have you attempted this one yet ?

  2. Alexalayne
    • 3 years ago
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    yeah

  3. LogicalApple
    • 3 years ago
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    \[f(x) = \sin ^{3}(x)\] 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
    • 3 years ago
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    I got f'(X) is 9x^2cosx^2

  5. Alexalayne
    • 3 years ago
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    that is 3u^2

  6. LogicalApple
    • 3 years ago
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    3u^2 du/dx, yes. Now what is du/dx if u = sin x?

  7. LogicalApple
    • 3 years ago
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    In other words, what is u' if u = sin x

  8. Alexalayne
    • 3 years ago
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    cosx^2

  9. LogicalApple
    • 3 years ago
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    What is the derivative of sin(x) ?

  10. Alexalayne
    • 3 years ago
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    COS

  11. LogicalApple
    • 3 years ago
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    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
    • 3 years ago
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    |dw:1357249368629:dw|

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