If $f(x)=5 \cos ^3 x-3 \sin ^2 x$ and $g(x)=4 \sin ^3 x+\cos ^2 x$, then the derivative of $f(x)$ with respect to $g(x)$ is

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Aicharya · Accepted Answer

$\begin{aligned} & \quad f(x)=5 \cos ^3 x-3 \sin ^2 x, g(x)=4 \sin ^3 x+\cos ^2 x \ & \frac{d f(x)}{d x}=-15 \cos ^2 x \sin x-6 \cos x \sin x \ & \frac{d g(x)}{d x}=12 \sin ^2 x \cos x-2 \cos x \sin x \ & \frac{d f(x)}{d g(x)}=\frac{-15 \cos ^2 x \sin x-6 \cos x \sin x}{12 \sin ^2 x \cos x-2 \cos x \sin x}=\frac{-15 \cos x-6}{12 \sin x-2}\end{aligned}$

If $f(x)=5 \cos ^3 x-3 \sin ^2 x$ and $g(x)=4 \sin ^3 x+\cos ^2 x$, then the derivative of $f(x)$ with…

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