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

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Answer 1 · 2016-05-28T20:24:19

$=>(dy)/(dx)=-cos(x)sin(sin(x))$

Let $u= sin(x)$

Then $(du)/dx= cos(x)$

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Let $y=cos(u)$

Then $(dy)/(du)=-sin(u)$

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But $(dy)/(dx)=(du)/(dx)xx(dy)/(du)$

$=>(dy)/(dx)=cos(x)xx(-sin(u))$

$=>(dy)/(dx)=-cos(x)sin(sin(x))$

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