# Differentiate the following functions with respect to $x:\; sinx(ax+b)$

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} $$= cosx Given y = sinx(ax+b): According to the Chain Rule for differentiation, given two functions f(x) and g(x), and y=f(g(x)) \rightarrow y' = f'(g(x)).g'(x) \; \large \frac{d(sinx)}{dx}$$= cosx$
$\Rightarrow$ Given $g(x) = ax+b \rightarrow g'(x) = a$
$\Rightarrow f'(g(x)) = f'(sin(ax+b) = cos(ax+b)$
$\Rightarrow$ $y' = f'(g(x)).g'(x) = cos(ax+b).a = a.cos(ax+b)$