Differentiation PYQs - Last 10 Years

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MathematicsCalculus2017-2026

All Differentiation PYQs Last 5 Years Create chapter test

Practice 38 KCET 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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Mathematics / Calculus

2017-2026

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Last 10 Years Differentiation Questions

Showing 38 of 38 filtered questions.

1Differentiation

If $\sqrt{x} \sqrt[3]{y} = (x + y)^n$ and $x\dfrac{dy}{dx} - y = 0$, then $n = $

2Differentiation

If $y = \sqrt[3]{\tan x + y}$, then $\dfrac{dy}{dx} = $

3Differentiation

If $f(x) = \sin^{-1}\left(\dfrac{2x}{1 + x^2}\right)$, then $f'\left(\dfrac{1}{2}\right) = $

4Differentiation

The second order derivative of $\cos^{-1}(4x^3 - 3x)$ with respect to $\cos^{-1}(2x^2 - 1)$, where $\dfrac{1}{2} < x < 1$ is

5Differentiation

The derivative of $\sin \mathrm{x}$ with respect to $\log \mathrm{x}$ is

6Differentiation

If $\mathrm{y}=\mathrm{a} \sin ^3 \mathrm{t}, \mathrm{x}=\mathrm{a} \cos ^3 \mathrm{t}$, then $\frac{\mathrm{dy}}{\mathrm{dx}}$ at $\mathrm{t}=\frac{3 \pi}{4}$ is

7Differentiation

If $y=\frac{\cos x}{1+\sin x}$, then
(a) $\frac{d y}{d x}=\frac{-1}{1+\sin x}$
(b) $\frac{d y}{d x}=\frac{1}{1+\sin x}$
(c) $\frac{\mathrm{dy}}{\mathrm{dx}}=-\frac{1}{2} \sec ^2\left(\frac{\pi}{4}-\frac{\mathrm{x}}{2}\right)$
(d) $\frac{\ma...

8Differentiation

$\frac{d}{d x}\left[\cos ^2\left(\cot ^{-1} \sqrt{\frac{2+x}{2-x}}\right)\right]$ is

9Differentiation

If $y=2 x^{3 x}$, then $d y / d x$ at $x=1$ is

10Differentiation

If \(f(x)\) and \(g(x)\) are two functions with \(g(x)=x-\frac{1}{x}\) and \(f \circ g(x)=x^3-\frac{1}{x^3}\), then \(f^{\prime}(x)\) is equals to

11Differentiation

If \(f(x)=1+n x+\frac{n(n-1)}{2} x^2+\frac{n(n-1)(n-2)}{6} x^3+\ldots+x^n\), then \(f^n(1)\) is equal to :

12Differentiation

If \(y=a \sin x+b \cos x\), then \(y^2+\left(\frac{d y}{d x}\right)^2\) is a

13Differentiation

If \(e^y+x y=e\) the ordered pair \(\left(\frac{d y}{d x}, \frac{d^2 y}{d x^2}\right)\) at \(x=0\) is equal to

14Differentiation

If \(y=x^{\sin x}+(\sin x)^x\), then \(\frac{d y}{d x}\) at \(x=\frac{\pi}{2}\) is

15Differentiation

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

16Differentiation

If \(y=e^{\sqrt{x \sqrt{x} \sqrt{x}}...,} x >1\), then \(\frac{d^2 y}{d x^2}\) at \(x=\log _e 3\) is

17Differentiation

If \(x=e^\theta \sin \theta, y=e^\theta \cos \theta\) where \(\theta\) is a parameter, then \(\frac{d y}{d x}\) at \((1,1)\) is equal to

18Differentiation

If \(y=\left(1+x^2\right) \tan ^{-1} x-x\), then \(\frac{d y}{d x}\) is

19Differentiation

If \(y=(x-1)^2(x-2)^3(x-3)^5\), then \(\frac{d y}{d x}\) at \(x=4\) is equal to

20Differentiation

If \(a\) and \(b\) are fixed non-zero constants, then the derivative of \(\frac{a}{x^4}-\frac{b}{x^2}+\cos x\) is \(m a+n b-p\), where

21Differentiation

If the parametric equation of curve is given by \(x=\cos \theta+\log \tan \frac{\theta}{2}\) and \(y=\sin \theta\), then the points for which \(\frac{d y}{d x}=0\) are given by

22Differentiation

For constant \(a, \frac{d}{d x}\left(x^x+x^a+a^x+a^a\right)\) is

23Differentiation

Consider the following statements
Statement 1 : If \(y=\log _{10} x+\log _e x\), then \(\frac{d y}{d x}=\frac{\log _{10} e}{x}+\frac{1}{x}\)
Statement 2 : If \(\frac{d}{d x}\left(\log _{10} x\right)=\frac{\log x}{\log 10}\) and $$\frac{d}{d...

24Differentiation

If \(y=\left(\cos x^2\right)^2\), then \(\frac{d y}{d x}\) is equal to

25Differentiation

If \((x e)^y=e^y\), then \(\frac{d y}{d x}\) is

26Differentiation

If \(y=2 x^{n+1}+\frac{3}{x^n}\), then \(x^2 \frac{d^{2 y}}{d x^2}\) is

27Differentiation

If \(2^x+2^y=2^{x+y}\), then \(\frac{d y}{d x}\) is

28Differentiation

\(\sqrt[3]{y} \sqrt{x}=\sqrt[6]{(x+y)^5}\), then \(\frac{d y}{d x}=\)

29Differentiation

If \(x=a \sec ^2 \theta\) & \(y=a \tan ^2 \theta\), then \(\frac{d^2 y}{d x^2}=\)

30Differentiation

If \([x]\) represents the greatest integer function and \(f(x)=x-[x]-\cos x\), then \(f^{\prime}\left(\frac{\pi}{2}\right)=\)

31Differentiation

If $\cos y=x \cos (a+y)$ with $\cos a \neq \pm 1$, then $\frac{d y}{d x}$ is equal to

32Differentiation

\(\text { If } y=\sqrt{x+\sqrt{x+\sqrt{x+\ldots \infty}}} \text {, then } \frac{d y}{d x} \text { is equal }\) to

33Differentiation

If $f(x)=|\cos x-\sin x|$, then $f^{\prime}\left(\frac{\pi}{6}\right)$ is equal to

34Differentiation

If $y=\tan ^{-1}\left(\frac{\sin x+\cos x}{\cos x-\sin x}\right)$, then $\frac{d y}{d x}$ is equal to

35Differentiation

If $\sin x=\frac{2 t}{1+t^2}, \tan y+\frac{2 t}{1-t^2}$, then $\frac{d y}{d x}$ is equal to

36Differentiation

If $y=\log (\log x)$, then $\frac{d^2 y}{d x^2}$ is equal to

37Differentiation

$$ \text { If } y=\left|\begin{array}{ccc} f(x) & g(x) & h(x) \\ l & m & n \\ a & b & c \end{array}\right| \text {, then } \frac{d y}{d x} \text { is equal to } $$

MCQM+1 / -02017

38Differentiation

The derivative of $\cos ^{-1}\left(2 x^2-1\right)$ w.r.t. $\cos ^{-1} x$ is