Question

How do you differentiate `f(x)=sin(cos(3x))`?

Answer 1

`f'(x)= -3sin(3x)cos(cos3x)`

Explanation:

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`f(x)` is composed of two functions `" "sinx " "and" "cosx`
`f(x)` is differentiated by applying chain rule .
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Let `u(x) = sinx" " and " "v(x)=cos3x`
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Then, `" "f(x)=u@v(x)`
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The differentiation of `f(x)` is :
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`f'(x)=(u@v(x))'=u'(v(x))xxv'(x)`
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Computing `u'(v(x))`
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`u'(x)=cosx`
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`u'(v(x))=cos(v(x))=cos(cos3x)`
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Computing `v'(x)`
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`v'(x)=-3sin3x`
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`f'(x)= cos(cos3x)xx (-3sin3x)`

`f'(x)= -3sin(3x)cos(cos3x)`