Differentiate sin left(cos left(x^{2}right)ri | vedclass

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Let $y = \sin \left(\cos \left(x^{2}\right)\right).$ Using the chain rule,we differentiate with respect to $x$: $\frac{dy}{dx} = \frac{d}{dx} \left[ \

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Vedclass · Answer

Let $y = \sin \left(\cos \left(x^{2}\right)\right).$
Using the chain rule,we differentiate with respect to $x$:
$\frac{dy}{dx} = \frac{d}{dx} \left[ \sin \left(\cos \left(x^{2}\right)\right) \right]$
$= \cos \left(\cos \left(x^{2}\right)\right) \cdot \frac{d}{dx} \left( \cos \left(x^{2}\right) \right)$
$= \cos \left(\cos \left(x^{2}\right)\right) \cdot \left( -\sin \left(x^{2}\right) \right) \cdot \frac{d}{dx} \left( x^{2} \right)$
$= \cos \left(\cos \left(x^{2}\right)\right) \cdot (-\sin \left(x^{2}\right)) \cdot (2x)$
$= -2x \sin \left(x^{2}\right) \cos \left(\cos \left(x^{2}\right)\right).$

Differentiate $\sin \left(\cos \left(x^{2}\right)\right)$ with respect to $x.$

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