List of top Mathematics Questions on Differentiation by taking log asked in CBSE CLASS XII

Differentiate \( x^x \) with respect to \( x \log x \).
Differentiate \(x^x\) with respect to \(x \log x\).
If \(xy = e^{x-y}\), then find \(\frac{dy}{dx}\).
If \( (\sin x)^y = y^{\cos x \), then find \( \frac{dy}{dx} \).}
If \( x^y = e^{x - y} \), prove that \( \frac{dy}{dx} = \frac{\log x}{(1 + \log x)^2} \):