List of top Mathematics Questions on Differentiation asked in AP EAPCET

If \[ y=\sec^{-1}\left(\frac{1+x^2}{2x}\right) \quad \text{and} \quad x>1, \] then \[ \frac{dy}{dx}= \]

If \[ f(x)=\sqrt{2^{2x}\log(3x-2)} \] then \(f'(2)=\)

If \(x \in [-1,1]\) and \(y=(\cot^{-1}x)^{\cot^{-1}x}\), then \(\left(\frac{dy}{dx}\right)_{x=0}=\)

If \(x=\sinh^{-1}t+\log(t^{2}+1)\) and \(y=\tan^{-1}t+\log|t|\), then \(\frac{dy}{dx}=\)

If \(f(x)=\sqrt{-(1+x)}\sec^{-1}x\) is a real valued function, then \(f'(x)=\)

If \( y=\text{sech}^{-1}\left(\frac{9}{9x^{2}+10}\right) \), then \( \frac{dy}{dx} = \)

If \( x^{2}y - xy^{2} + x^{3} - y^{3} = 0 \), then \( \frac{dy}{dx} \) at the point (1, 1) is

If $\tan^{-1}x^{2}+\tan^{-1}y^{2}=\frac{\pi}{2}$, then $\left(\frac{dy}{dx}\right)_{(-1,2)}=$

If $f(x)=\begin{cases}\frac{1-\sin^{3}x}{3\cos^{2}x}, & x\ne\frac{\pi}{2} \\ \frac{1}{2}, & x=\frac{\pi}{2}\end{cases}$, then $f^{\prime}\left(\frac{\pi}{2}\right)=$

If $y = \sqrt{\tan x + \sqrt{\tan x + \sqrt{\tan x + \dots \infty}}}$, then $(2y - 1)\frac{dy}{dx} =$

If $y = e^{a \sin^{-1} x}$, then $(1 - x^2) y_2 - x y_1 =$

If $y = \tan^{-1}\left(\frac{\sin x + \cos x}{\cos x - \sin x}\right)$, then $\frac{dy}{dx} = $

If $x = a \cos^3 t$ and $y = a \sin^3 t$, then the value of $\frac{dy}{dx}$ at $t = \frac{\pi}{4}$ is:

Gas is being pumped into a spherical balloon at the rate of $ 30 \, \text{ft}^3/\text{min} $. Then the rate at which the radius increases when it reaches the value $ 15 \, \text{ft} $ is:

If \[ \frac{d}{dx}\left(\frac{x^2+1}{(x^2+5)(x^2+9)}\right) = \frac{2x(x^2+1)}{(x^2+5)(x^2+9)} \left[ \frac{1}{f(x)}-\frac{1}{g(x)}-\frac{1}{h(x)} \right], \] then \(2h(x)-f(x)-g(x)=\)

The set of all \(x\) for which \[ \sin x\leq x \] is

Which of the following is differentiable at \(x=0\)?

If \[ \frac{d}{dx} \left( \frac{(x+1)^2\sqrt{x-1}} {(x+4)^3e^x} \right) = f(x) \left[ \frac{2}{x+1} +\frac{1}{2(x-1)} -\frac{3}{x+4} -1 \right], \] then \(f(5)=\)

If \[ y=\tan(3\tan^{-1}x), \] then \[ (1-3x^2)\frac{d^2y}{dx^2}-12x\frac{dy}{dx} \] is equal to:

If \[ \frac{y}{x}\cos^4\alpha+\frac{x}{y}\sin^4\alpha = 2\sin^2\alpha\cos^2\alpha, \] then \[ \frac{dy}{dx}= \]

If \[ \frac{d}{dx} \left[ A\log\left(\frac{\sqrt{1-x^3}+B}{\sqrt{1-x^3}+1}\right) \right] = \frac{1}{x\sqrt{1-x^3}}, \] then \(AB=\)

If \[ \frac{d^n y}{dx^n}=y_n \] and \[ y=e^{\sqrt{x}}+e^{-\sqrt{x}}, \] then \[ 4xy_2+2y_1= \]

If \[ 3f(\cos x)+2f(\sin x)=5x, \] then \[ f'(\cos x)+f'(\sin x)= \]

Assertion (A): \[ \frac{d}{dx}\left(\frac{x^2\sin x}{\log x}\right) = \frac{x^2\sin x}{\log x} \left(\cot x+\frac{2}{x}-\frac{1}{x\log x}\right) \] Reason (R): \[ \frac{d}{dx}\left(\frac{uv}{w}\right) = \frac{uv}{w} \left[ \frac{u'}{u}+\frac{v'}{v}-\frac{w'}{w} \right] \]

\[ \frac{d}{dx}\left[ \lim_{y\to 2} \frac{1}{y-2} \left( \frac{1}{x} - \frac{1}{x+y-2} \right) \right] \]