AP EAMCET · Maths · Differentiation
Assertion (A) \(\frac{d}{d x}\left(\frac{x^2 \sin x}{\log x}\right)=\frac{x^2 \sin x}{\log x}\) \(\left(\cot x+\frac{2}{x}-\frac{1}{x \log x}\right)\)
\(\operatorname{Reason}(\mathbf{R}) \frac{d}{d x}\left(\frac{u v}{w}\right)=\frac{u v}{w}\left[\frac{u^{\prime}}{u}+\frac{v^{\prime}}{v}+\frac{w^{\prime}}{w}\right]\)
- A \(A\) is true, \(R\) is true and \(R\) is correct explanation of A
- B \(A\) is true, \(R\) is true and \(R\) is not correct explanation of \(A\)
- C \(A\) is true, \(R\) is not correct
- D \(A\) is not correct, \(R\) is correct
Answer & Solution
Correct Answer
(A) \(A\) is true, \(R\) is true and \(R\) is correct explanation of A
Step-by-step Solution
Detailed explanation
Assertion : \(\frac{d}{d x}\left(\frac{x^2 \sin x}{\log x}\right)\) \(\begin{aligned} & =\frac{(\log x)\left[x^2 \cos x+2 x \sin x\right]-x \sin x}{(\log x)^2} \\ & =\frac{x^2 \cos x \log x+2 x \sin x \log x-x \sin x}{(\log x)^2}\end{aligned}\)…
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