Find the Derivative minus d First, divide dx cos(x) to the power of two

$\cos^{2} (x)$

Differentiate using the chain rule, which states that $\frac{d}{d x} [f (g (x))]$ is $f' (g (x)) g' (x)$ where $f (x) = x^{2}$ and $g (x) = \cos (x)$ .

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To apply the Chain Rule, set $u$ as $\cos (x)$ .

$\frac{d}{d u} [u^{2}] \frac{d}{d x} [\cos (x)]$

Differentiate using the Power Rule which states that $\frac{d}{d u} [u^{n}]$ is $n u^{n - 1}$ where $n = 2$ .

$2 u \frac{d}{d x} [\cos (x)]$

Replace all occurrences of $u$ with $\cos (x)$ .

$2 \cos (x) \frac{d}{d x} [\cos (x)]$

The derivative of $\cos (x)$ with respect to $x$ is $- \sin (x)$ .

$2 \cos (x) (- \sin (x))$

First, multiply $- 1$ by $2$ .

$- 2 \cos (x) \sin (x)$

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