Browse Questions

# Differentiate the functions with respect to x: $\; sin ( x^2 + 5 )$

$\begin{array}{1 1} 2cos(x^2+5)\\ 2x.cos(x^2+5) \\ 2x.cos(x^2-5) \\ 2.cos(x^2+5)\end{array}$

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} $$= cosx Given y = sin(x^2+5): According to the Chain Rule for differentiation, given two functions f(x) and g(x), and y=f(g(x)) \rightarrow y' = f'(g(x)).g'(x) \Rightarrow Given g(x) = x^2 + 5 \rightarrow g'(x) = 2x^{2-1} = 2x \; \large \frac{d(sinx)}{dx}$$= cosx$
$\Rightarrow f'(g(x)) = f'(cos (x^2+5))$
Therefore $y' = f'(g(x)).g'(x) = cos(x^2+5). 2x = 2x.cos(x^2+5)$