List of top Mathematics Questions on Calculus asked in CUET (UG)

If \( y = \frac{x^2}{1 + x^{b-a} + x^{c-a}} + \frac{x^2}{1 + x^{a-b} + x^{c-b}} + \frac{x^2}{1 + x^{a-c} + x^{b-c}} \), then \( \frac{dy}{dx} \) is:

If $x=t^{2}, y=t^{3}$, then $\frac{d^{2}y}{dx^{2}}$ is:

If \( y = \sqrt{x} + \frac{1}{\sqrt{x}} \), then \( 2x \frac{dy}{dx} \) is equal to

If \[ y= \left( x^{\sin x} \right)^{\tan x}, \] then find \[ \dfrac{dy}{dx}. \]

If \[ f(x)=\left(\frac{1+\sin x}{1-\sin x}\right)^{\tan x}, \] then find \[ \lim_{x\to0}\frac{\ln f(x)}{x^2}. \]

If \[ y = \left(\dfrac{x+1}{x-1}\right)^x, \] then find \(\dfrac{dy}{dx}\).

For \(y = x^3 - 3x^2 + 2\), slope at \(x=2\):

Differentiate: \( y = x^2\sin x \)