List of top Mathematics Questions on Derivatives asked in AP EAPCET

If \[ f(x)=\frac1{x^2}\int_{3}^{x}\left(2t-3f'(t)\right)\,dt, \] then \[ f'(3)= \]
If \[ y= \tan^{-1}\!\left(\frac{1}{1+x+x^2}\right) + \tan^{-1}\!\left(\frac{1}{x^2+3x+3}\right) + \tan^{-1}\!\left(\frac{1}{x^2+5x+7}\right), \] then \[ y'(0)= \]
If \(f\) is a derivable function and \[ 2f(\sin x)+f(\cos x)=x \qquad \forall x\in \mathbb{R}, \] then \[ f'(x)= \]
If $x^2 + y^2 + \sin y = 4$, then the value of $\frac{d^2y}{dx^2}$ at $x=-2$ is
If $y = \frac{x^4\sqrt{3x-5}}{\sqrt{(x^2-3)(2x-3)}}$, then $\frac{dy}{dx}|_{x=2} =$
The maximum value of $ a $ such that the second derivative of $ x^4 + ax^3 + \frac{3x^2}{2} + 1 $ is positive for all real $ x $ is
Let $ f : \mathbb{R} \to \mathbb{R} $ be a continuous function. If $ px + my + n = 0 $ is a tangent drawn to the curve $ y = f(x) $ at $ x = \alpha $, then at $ x = 0 $, the value of \[ \frac{d}{dx} \left( f(\alpha e^{2x}) \right) \]
If \[ x\sin(\alpha+y)=\sin y \] and \[ y=\frac{m}{x^2+2nx+1}, \] then \(m^2=\)
The function $ y = x^3 - ax^2 + 48x + 7 $ is increasing for all real values of $ x $. Find the interval in which $ a $ lies:
If $ a, b>0 $, then the minimum value of: $$ y = \frac{b^2}{a - x} + \frac{a^2}{x},\quad \text{for } 0<x<a $$

Find the derivative of the function \(f(x) = \sqrt{3x^2 + 2x + 1}\).