Find the derivative: frac{d}{dx}[cos((1 - x^2 | vedclass

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Question

(C) To find the derivative of $\cos((1 - x^2)^2)$,we use the chain rule.Let $y = \cos((1 - x^2)^2)$.Applying the chain rule: $\frac{dy}{dx} = -\sin((1

Vedclass · Accepted Answer

$4x(1 - x^2)\sin((1 - x^2)^2)$

Vedclass · Answer

(C) To find the derivative of $\cos((1 - x^2)^2)$,we use the chain rule.Let $y = \cos((1 - x^2)^2)$.Applying the chain rule: $\frac{dy}{dx} = -\sin((1 - x^2)^2) \cdot \frac{d}{dx}((1 - x^2)^2)$.Now,differentiate $(1 - x^2)^2$ using the power rule and chain rule:$\frac{d}{dx}((1 - x^2)^2) = 2(1 - x^2) \cdot \frac{d}{dx}(1 - x^2) = 2(1 - x^2) \cdot (-2x) = -4x(1 - x^2)$.Substituting this back into the expression:$\frac{dy}{dx} = -\sin((1 - x^2)^2) \cdot (-4x(1 - x^2)) = 4x(1 - x^2)\sin((1 - x^2)^2)$.Thus,the correct option is $C$.

Find the derivative: $\frac{d}{dx}[\cos((1 - x^2)^2)] = ?$

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