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Question
Differentiate \[x^\left( \sin x - \cos x \right) + \frac{x^2 - 1}{x^2 + 1}\] ?
Solution
\[\text{Let y } = x^\left( \sin x - \cos x \right) + \left( \frac{x^2 - 1}{x^2 + 1} \right)\]
\[ \Rightarrow y = e^{\log x^\left( \sin x - \cos x \right)} + \left( \frac{x^2 - 1}{x^2 + 1} \right)\]
\[ \Rightarrow y = e^{ \left( \sin x - \cos x \right)\log x } + \left( \frac{x^2 - 1}{x^2 + 1} \right)\]
Differentiate it with respect to x using chain rule,
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