AP EAMCET · Maths · Differentiation
The rate of change of \(x^{\sin x}\) with respect to \((\sin x)^{\mathrm{x}}\) is
- A \(\frac{x^{\sin x}\left(\frac{\sin x}{x}+\cos x \cdot \log x\right)}{(\sin x)^x(x \cdot \cot x+\log \sin x)}\)
- B \(\frac{x^{\sin x}(x \cot x+\log \sin x)}{x^{\sin x}\left(\frac{\sin x}{x}+\cos x \cdot \log x\right)}\)
- C \(y\left(\frac{\sin x}{x}+\cos x \cdot \log x\right)\)
- D \((\sin x)^{\mathrm{x}}(x \cot x+\log \sin x)\)
Answer & Solution
Correct Answer
(A) \(\frac{x^{\sin x}\left(\frac{\sin x}{x}+\cos x \cdot \log x\right)}{(\sin x)^x(x \cdot \cot x+\log \sin x)}\)
Step-by-step Solution
Detailed explanation
Let \(\mathrm{u}=x^{\sin x} \Rightarrow \log \mathrm{u}=\sin x \log x^{\prime}\) Differentiating w.r.t. \(x\)…
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