List of top Mathematics Questions on Differentiation asked in PSEB XII

When \( x = at^2 \), \( y = 2at \), then \( \frac{dy}{dx} \) is:
If \( y = \tan x \), then at \( x = \frac{\pi}{4} \), \[ \frac{dy}{dx} = \quad ......... \]
Differentiate \( x \sin x + (\sin x)^x \) with respect to \( x \).
If \( y = (\tan^{-1} x)^2 \), prove that \( (x^2 + 1)^2 y_2 + 2x (x^2 + 1) y_1 = 2 \).
If \( y = e^x \), then \( \frac{d^2y}{dx^2} \) is:
If \( x = \frac{1 - t^2}{1 + t^2} \), \( y = \frac{2t}{1 + t^2} \), then prove that \( \frac{dy}{dx} + \frac{x}{y} = 0 \).
If \( y = x^{\sin x} + (\sin x)^x \), then find \( \frac{dy}{dx} \).
Find \( \frac{dy}{dx} \), if \( x^3 + 2x^2 y - 3xy^2 + y^3 = 100 \)
If \( y = \log x \), then \( \frac{dy}{dx} \) is:
If \( y = e^{\log x} \), then \( \frac{dy}{dx} \) is:
If \( y = \tan x \), then at \( x = \frac{\pi}{4} \), \( \frac{dy}{dx} \) is equal to: