List of top Mathematics Questions on Differentiation by taking log

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 \( \frac{dy}{dx} \).}

Find \[ \frac{dy}{dx} \] if \[ y=\log(\sin x). \]

Which of the following functions has derivative equal to \( \cos x \)?

If \( x^y = e^{x - y} \), prove that \( \frac{dy}{dx} = \frac{\log x}{(1 + \log x)^2} \):

If log₃2,log₃(2^x-5) and log₃(2^x-7/2) are in A.P., then x is equal to

Find the differential coefficient of \[ y = x^x + (\cos x)^{\tan x}. \]

Differentiate $y = (\cos x)^{\tan x} + x^{x}$.