AP EAMCET · Maths · Differentiation
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
- A \(\frac{5 \cos x+2}{6 \cos x-1}\)
- B \(-\left(\frac{5 \cos x+2}{6 \cos x-1}\right)\)
- C \(\frac{15 \cos x-6}{12 \sin x+2}\)
- D \(-\left(\frac{15 \cos x+6}{12 \sin x-2}\right)\)
Answer & Solution
Correct Answer
(D) \(-\left(\frac{15 \cos x+6}{12 \sin x-2}\right)\)
Step-by-step Solution
Detailed explanation
\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…
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