List of top Mathematics Questions on Logarithmic Differentiation asked in KEAM

If $y=(\tan x)^{x}$, then $\frac{1}{y}\frac{dy}{dx}=$ ________.

Find $ \frac{dy}{dx} $ for the equation: $ y = \cos x \times \sin y $

Evaluate the derivative of $ y = \cos x \times \sin y, \quad \frac{dy}{dx} \text{ at } \left( \frac{\pi}{6}, \frac{\pi}{5} \right) $

If \[ x^4 + 2\sqrt{y} + 1 = 3, \] then \( \frac{dy}{dx} \) at \( (1,0) \) is equal to

If \[ y = \log_e \left( \frac{1 + 2x^2}{1 - 3x^2} \right), \] then \( \frac{dy}{dx} \) is:

Evaluate the integral: \[ \int \frac{6x^3 + 9x^2}{x^4 + 3x^3 - 9x^2} dx. \]

Let \(f(x) =   \begin{cases}     \tan x,       & if\ 0\leq x\leq \frac{\pi}{4} \\      ax+b,       & if\ \frac{\pi}{4}\lt x\lt \frac{\pi}{2}   \end{cases}\), If f(x) is differentiable at \(x=\frac{\pi}{4}\), then the values of a and b are respectively

If \(y=e^{3\log(2x+1)}\), then \(\frac{dy}{dx}=\)