Differentiate the function with respect to x: $cos\;(sin x)$

$\begin{array}{1 1} -cosx.sin(sinx) \\ cosx.sin(sinx) \\ -sinx.sin(cosx) \\ -cosx.sin(cosx) \end{array}$

Toolbox:
• According to the Chain Rule for differentiation, given two functions $f(x)$ and $g(x)$, and $y=f(g(x)) \rightarrow y' = f'(g(x)).g'(x)$.
• $\; \large \frac{d(sinx)}{dx} $$= cosx • \; \large \frac{d(cosx)}{dx}$$= -sinx$
Given $y = cos (sinx)$
According to the Chain Rule for differentiation, given two functions $f(x)$ and $g(x)$, and $y=f(g(x)) \rightarrow y' = f'(g(x)).g'(x)$
$\; \large \frac{d(sinx)}{dx} $$= cosx and \; \large \frac{d(cosx)}{dx}$$= -sinx$
$\Rightarrow$ Given $g(x) = sinx \rightarrow g'(x) = cosx$
$\Rightarrow f'(g(x)) = f'(cos (sinx)) = -sin(sinx)$
$\Rightarrow$ $y' = f'(g(x)).g'(x) = -sin(sinx).cosx = -cosx.sin(sinx)$
answered Apr 4, 2013