Find the derivative: frac{d}{dx}{ cos(sin(x^2 | vedclass

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(B) To find the derivative of $y = \cos(\sin(x^2))$,we use the chain rule.Let $u = \sin(x^2)$ and $v = x^2$.Then $y = \cos(u)$,$u = \sin(v)$,and $v =

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

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(B) To find the derivative of $y = \cos(\sin(x^2))$,we use the chain rule.Let $u = \sin(x^2)$ and $v = x^2$.Then $y = \cos(u)$,$u = \sin(v)$,and $v = x^2$.Applying the chain rule: $\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dv} \cdot \frac{dv}{dx}$.$\frac{dy}{du} = -\sin(u) = -\sin(\sin(x^2))$.$\frac{du}{dv} = \cos(v) = \cos(x^2)$.$\frac{dv}{dx} = 2x$.Multiplying these together: $\frac{dy}{dx} = -\sin(\sin(x^2)) \cdot \cos(x^2) \cdot 2x$.Thus,the correct option is $B$.

Find the derivative: $\frac{d}{dx}\{ \cos(\sin(x^2)) \}$

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