Find the Derivative - d/dθ cos(theta^2)

$\cos (θ^{2})$

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

To apply the Chain Rule, set $u$ as $θ^{2}$ .

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

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

$- \sin (u) \frac{d}{d θ} [θ^{2}]$

Replace all occurrences of $u$ with $θ^{2}$ .

$- \sin (θ^{2}) \frac{d}{d θ} [θ^{2}]$

Differentiate using the Power Rule.

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

$- \sin (θ^{2}) (2 θ)$

Simplify the expression.

Multiply $2$ by $- 1$ .

$- 2 \sin (θ^{2}) θ$

Reorder the factors of $- 2 \sin (θ^{2}) θ$ .

$- 2 θ \sin (θ^{2})$

Find the Derivative - d/dθ cos(theta^2)

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