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



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LogicalApple
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Have you attempted this one yet ?

Alexalayne
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yeah

LogicalApple
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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

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

Alexalayne
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that is 3u^2

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

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

Alexalayne
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cosx^2

LogicalApple
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What is the derivative of sin(x) ?

Alexalayne
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COS

LogicalApple
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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 ?

LogicalApple
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dw:1357249368629:dw