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

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Answer 1 · 2016-05-28T20:24:19

$\Rightarrow \frac{d y}{d x} = - cos (x) sin (sin (x))$ $=>(dy)/(dx)=-cos(x)sin(sin(x))$

Let $u = sin (x)$ $u= sin(x)$

Then $\frac{d u}{d x} = cos (x)$ $(du)/dx= cos(x)$

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Let $y = cos (u)$ $y=cos(u)$

Then $\frac{d y}{d u} = - sin (u)$ $(dy)/(du)=-sin(u)$

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But $\frac{d y}{d x} = \frac{d u}{d x} \times \frac{d y}{d u}$ $(dy)/(dx)=(du)/(dx)xx(dy)/(du)$

$\Rightarrow \frac{d y}{d x} = cos (x) \times (- sin (u))$ $=>(dy)/(dx)=cos(x)xx(-sin(u))$

$\Rightarrow \frac{d y}{d x} = - cos (x) sin (sin (x))$ $=>(dy)/(dx)=-cos(x)sin(sin(x))$

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