Differentiation PYQs - Last 5 Years

MHT CET / Mathematics / Calculus / 185 recent questions

MathematicsCalculus2022-2026

All Differentiation PYQs Last 10 Years Create chapter test

Practice 185 MHT CET Mathematics questions from Differentiation. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

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Last 5 Years Differentiation Questions

Showing 50 of 185 filtered questions.

1Differentiation

If $y = \tan^{-1}\left(\dfrac{1}{x^2+x+1}\right) + \tan^{-1}\left(\dfrac{1}{x^2+3x+3}\right) + \tan^{-1}\left(\dfrac{1}{x^2+5x+7}\right) + \ldots$ upto $n$ terms, then $y'(0) =$

2Differentiation

If $y = \sin(e^{\log 2x})$, then the value of $\dfrac{dy}{dx}$ at $x = \dfrac{\pi}{2}$ is

3Differentiation

If $y = \sqrt{x + \sqrt{x^2 + 1}}$, then the value of $\dfrac{dy}{dx}$ is

4Differentiation

If $y = \sqrt{\tan x + \sqrt{\tan x + \sqrt{\tan x + \cdots \cdots \cdots \infty}}}$, then $\left(\dfrac{dy}{dx}\right)^2$ at $x = \dfrac{\pi}{4}$ is

5Differentiation

If $y = \sqrt{x^2 + 8x + 3}$, then the value of $\dfrac{d^2 y}{dx^2}$ at $x = 3$ is

6Differentiation

If $y = f\left(\dfrac{3 + 2x}{3 - 2x}\right)$, where $f(x) = \tan(\log x)$ and $\dfrac{dy}{dx} = \left(\dfrac{A}{B + C x^2}\right) \cdot \sec^2\left(\log\left(\dfrac{3 + 2x}{3 - 2x}\right)\right)$, then the respective values of A, B and C a...

7Differentiation

If $x = \sin(t), y = \cos(pt)$, then $(1 - x^2)\dfrac{d^2 y}{dx^2} - x\dfrac{dy}{dx} = $

8Differentiation

If $x^3 + y^3 = 6$ and $\dfrac{d^2y}{dx^2} \cdot \dfrac{d^2x}{dy^2} = \dfrac{m}{(xy)^n}$, where $m, n \in R$ then $\dfrac{m}{n} = $

9Differentiation

If the derivative of $\tan^{-1}(a + bx)$ with respect to x at $x = 0$ is $1$, then $a^6 - b^3 = $

10Differentiation

The derivative of $\tan^{-1}\left(\dfrac{\sqrt{1+x^2} - 1}{x}\right)$ with respect to $\sin^{-1}\left(\dfrac{2x}{1+x^2}\right)$ is...

11Differentiation

If $x \cdot \log _e\left(\log _e x\right)-x^2+y^2=4(y>0)$, then $\frac{d y}{d x}$ at $x=\mathrm{e}$ is

12Differentiation

Derivative of
$y=\sqrt{\sin x+\sqrt{\sin x+\sqrt{\sin x+\ldots \ldots \ldots \ldots \ldots \ldots \infty}}}$ is

13Differentiation

If $\mathrm{f}(x)=\sqrt{1+\cos ^2\left(x^2\right)}$, then $\mathrm{f}^{\prime}\left(\frac{\sqrt{\pi}}{2}\right)$ is

14Differentiation

If $\mathrm{f}(x)=\frac{\sin ^2 x}{1+\cot x}+\frac{\cos ^2 x}{1+\tan x}$, then the value of $\mathrm{f}^{\prime}\left(\frac{\pi}{6}\right)$ is equal to

15Differentiation

If $\mathrm{f}(x)=3 x^2+2 x \mathrm{f}^{\prime}(1)+\mathrm{f}^{\prime \prime}(2)$, then $\mathrm{f}(x)=\ldots \ldots .$.

16Differentiation

If $u=\log (\sqrt{x-1}-\sqrt{x+1})$ and $v=\sqrt{x+1}+\sqrt{x-1}$ then $\frac{d u}{d v}=\ldots$.

17Differentiation

If $\frac{x^2}{\mathrm{a}^2}+\frac{y^2}{\mathrm{~b}^2}=1$, then $\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}$ is

18Differentiation

If
\(\sqrt{y-\sqrt{y-\sqrt{y-\ldots \ldots \ldots \infty}}}=\sqrt{x+\sqrt{x+\sqrt{x+\ldots \ldots \ldots \infty}}}\)
then $\frac{\mathrm{d} y}{\mathrm{~d} x}=$

19Differentiation

If $y=\tan ^{-1}\left(\frac{12 x-64 x^3}{1-48 x^2}\right)$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}=$

20Differentiation

If $y=\tan ^{-1}\left[\frac{4 \sin 2 x}{\cos 2 x-6 \sin ^2 x}\right]$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ at $x=0$ is

21Differentiation

If $y=\sqrt{x+\sqrt{y+\sqrt{x+\sqrt{y+\ldots \ldots \ldots \ldots \ldots \ldots . \infty}}}}$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}=$

22Differentiation

If $x=a \sin 2 t(1+\cos 2 t), y=b \cos 2 t(1-\cos 2 t)$ then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ is equal to

23Differentiation

If $x=\mathrm{e}^{\tan ^{-1}\left(\frac{y-x^2}{x^2}\right)}$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ at $x=1$ is

24Differentiation

If $x=\sin \theta, y=\sin ^3 \theta$, then $\frac{d^2 y}{d x^2}$ at $\theta=\frac{\pi}{6}$ is

25Differentiation

If $\mathrm{f}(x)=3 x^3+2 x^2 \mathrm{f}^{\prime}(1)+x \mathrm{f}^{\prime \prime}(2)+\mathrm{f}^{\prime \prime \prime}(3)$ then $\mathrm{f}(x)=$ __________ .

26Differentiation

For $N \in \mathbb{N}, \frac{\mathrm{~d}^{\mathrm{n}}}{\mathrm{d} x^{\mathrm{n}}}(\log x)=$

27Differentiation

If $x=\operatorname{acos}^3 \theta y=\operatorname{asin}^3 \theta$
Then $\sqrt{1+\left(\frac{\mathrm{d} y}{\mathrm{~d} x}\right)^2}=$

28Differentiation

Derivative of $x^{\left(x^x\right)}$ is

29Differentiation

If $\mathrm{f}(1)=3, \mathrm{f}^{\prime}(1)=2$, then $\frac{\mathrm{d}}{\mathrm{dx}}\left\{\log \left[\mathrm{f}\left(\mathrm{e}^x+2 x\right)\right]\right\}$ at $x=0$ is

30Differentiation

If $y=\frac{\mathrm{K}^{\cos ^{-1} x}}{1+\mathrm{K}^{\cos ^{-1} x}}$ and $\mathrm{t}=\mathrm{K}^{\cos ^{-1} x}$, then $\frac{\mathrm{d} y}{\mathrm{dt}}=$

31Differentiation

If $(\mathrm{a}+\mathrm{b} x) \mathrm{e}^{\frac{y}{x}}=x$, then $x^3 \frac{\mathrm{~d}^2 y}{\mathrm{~d} x^2}$ is equal to

32Differentiation

If $x=\log \mathrm{t}, \mathrm{t}>0$ and $y=\frac{1}{\mathrm{t}}$ then $\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}=$

MCQM+2 / -02025

33Differentiation

If $y=\mathrm{a}^x \cdot \mathrm{~b}^{2 x-1}$, then $\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}$ is equal to

34Differentiation

If $y=\sin ^2\left(\cot ^{-1}\left(\sqrt{\frac{1-x}{1+x}}\right)\right)$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}=$

35Differentiation

If $\mathrm{y}=x^x+x^{\frac{1}{x}}$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ is equal to

36Differentiation

If $f(1)=1, f^{\prime}(1)=3$, then the derivative of $\mathrm{f}(\mathrm{f}(\mathrm{f}(x)))+(\mathrm{f}(x))^2$ at $x=1$ is

37Differentiation

If $y=\log _{\mathrm{e}} x^3+3 \sin ^{-1} x+\mathrm{kx}^2$ and $y^{\prime}\left(\frac{1}{2}\right)=2 \sqrt{3}$, then $k=$

38Differentiation

If $u=\frac{\tan ^{-1} x}{\tan ^{-1} x+1}$ and $v=\tan ^{-1}\left(\tan ^{-1} x\right)$ then $\frac{d u}{d v}=$

39Differentiation

If $x^y+y^x=\mathrm{a}^{\mathrm{b}}$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ at $x=1, y=2$ is

40Differentiation

If $\mathrm{a}\left(4+x^2\right)=x$ and $y-x^3=\mathrm{a}^2$ then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ at $x=1$ is $\qquad$

41Differentiation

For $\mathrm{n} \in \mathbb{N}$ if $y=\mathrm{a} x^{\mathrm{n}+1}+\mathrm{b} x^{-\mathrm{n}}$, then $x^2 \frac{\mathrm{~d}^2 y}{\mathrm{~d} x^2}=$

42Differentiation

The derivative of $\tan ^{-1}\left(\sqrt{1+x^2}-1\right)$ is

43Differentiation

The derivative of
\(y=(1-x)(2-x) \ldots \ldots \ldots \ldots \ldots \ldots(\mathrm{n}-x)\)
at $x=1$ is

44Differentiation

If $x^{\frac{2}{5}}+y^{\frac{2}{5}}=\mathrm{a}^{\frac{2}{5}}$ then $\frac{\mathrm{d} y}{\mathrm{~d} x}=$

45Differentiation

The first derivative of the function $\left(\cos ^{-1}\left(\sin \sqrt{\frac{1+x}{2}}\right)+x^x\right)$ with respect to $x$ at $x=1$ is

46Differentiation

If $\mathrm{f}(x)=\frac{x^2-x}{x^2+2 x}$ then $\frac{\mathrm{d}}{\mathrm{d} x}\left(\mathrm{f}^{-1}(x)\right)$ at $x=2$ is

47Differentiation

Derivative of $\mathrm{e}^x$ w.r.t. $\sqrt{x}$ is

48Differentiation

If for $x \in\left(0, \frac{1}{4}\right)$, the derivative of $\tan ^{-1}\left(\frac{6 x \sqrt{x}}{1-9 x^3}\right)$ is $\sqrt{x} \cdot g(x)$, then $g(x)$ equals

49Differentiation

If $\log (x+y)=\sin (x+y)$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ is

50Differentiation

Let $\mathrm{f}(x)=\mathrm{e}^x, \mathrm{~g}(x)=\sin ^{-1} x$ and $\mathrm{h}(x)=\mathrm{f}(\mathrm{g}(x))$, then $\left(\frac{h^{\prime}(x)}{h(x)}\right)^2$ is equal to