The derivative of cos^{3} x with respect to s | vedclass

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Question

(A) Let $u = \cos^{3} x$ and $v = \sin^{3} x$. Applying the chain rule,we find the derivatives with respect to $x$: $\frac{du}{dx} = 3 \cos^{2} x (-\s

Vedclass · Accepted Answer

$-\cot x$

Vedclass · Answer

(A) Let $u = \cos^{3} x$ and $v = \sin^{3} x$. Applying the chain rule,we find the derivatives with respect to $x$: $\frac{du}{dx} = 3 \cos^{2} x (-\sin x) = -3 \cos^{2} x \sin x$ $\frac{dv}{dx} = 3 \sin^{2} x (\cos x) = 3 \sin^{2} x \cos x$ Now,the derivative of $u$ with respect to $v$ is given by: $\frac{du}{dv} = \frac{du/dx}{dv/dx} = \frac{-3 \cos^{2} x \sin x}{3 \sin^{2} x \cos x}$ Simplifying the expression: $\frac{du}{dv} = -\frac{\cos x}{\sin x} = -\cot x$

The derivative of $\cos^{3} x$ with respect to $\sin^{3} x$ is

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