The differential coefficient of sin(cos(x2)) with respect to x is :

Question

The differential coefficient of $\sin (\cos (x^{2}))$ with respect to $x$ is :

Smart Achievers · Accepted Answer

(1)

Ans. $- 2 x s i n (x^{2}) c o s (c o s (x^{2}))$

Explanation:

We have, $y = \sin (\cos (x^{2}))$

Therefore, $\frac{d y}{d x} = \frac{d}{d x} [\sin (\cos (x^{2}))]$

$= \cos (\cos (x^{2})) \cdot \frac{d}{d x} (\cos (x^{2}))$

$= \cos (\cos (x^{2})) (- \sin (x^{2})) \cdot \frac{d}{d x} (x^{2})$

$= - \sin (x^{2}) \cos (\cos (x^{2})) (2 x)$

$= - 2 x \sin (x^{2}) \cos (\cos (x^{2}))$

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