Differentiation PYQs - Last 5 Years

COMEDK / Mathematics / Calculus / 24 recent questions

MathematicsCalculus2022-2026

All Differentiation PYQs Last 10 Years Create chapter test

Practice 24 COMEDK Mathematics questions from Differentiation. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

24

PYQs on Page

Mathematics / Calculus

2023-2026

Year Range

Based on indexed question metadata

24

Last 5 Years

2022-2026

24

Last 10 Years

2017-2026

Recent Year Trend

2023

2024

2025

2026

20238 max PYQs/year2026

Question Types

24PYQs

MCQ100%

Difficulty Mix

#1 Unknown24

24 in last 5 years24 in last 10 years

Last 5 Years Differentiation Questions

Showing 24 of 24 filtered questions.

1Differentiation

The derivative of $y=\sin ^2\left[\cot ^{-1}\left(\sqrt{\frac{\mathbf{1}-\boldsymbol{x}}{\mathbf{1}+\boldsymbol{x}}}\right)\right]$ is

2Differentiation

\(\text { If } x=a(\theta-\sin \theta) \text { and } y=a(1-\cos \theta) \text {, then } \frac{\left(\mathbf{1}+\boldsymbol{y}_{\mathbf{1}}{ }^{\mathbf{2}}\right)^{\mathbf{3} / \mathbf{2}}}{\boldsymbol{y}_{\mathbf{2}}}=\)

3Differentiation

If $\log y=\log (\sin x)-x^2$, then $\frac{d^2 y}{d x^2}+\mathbf{4} x \frac{d y}{d x}+\mathbf{4} x^2 y=$

4Differentiation

\(\text { If } y=\tan ^{-1}\left(\frac{\sqrt{1+x^3}+\sqrt{1-x^3}}{\sqrt{1+x^3}-\sqrt{1-x^3}}\right) \text { then } \frac{\boldsymbol{d} \boldsymbol{y}}{\boldsymbol{d x}}=\)

5Differentiation

\(\text { The second derivative of } \sin 3 \boldsymbol{x} \boldsymbol{\operatorname { c o s }} \mathbf{5 x} \text { is: }\)

6Differentiation

If $f(x)=\left(\frac{3+x}{1+x}\right)^{2+3 x}$, then $f^{\prime}(0)=$

7Differentiation

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

8Differentiation

If $y=\sqrt{\frac{x}{a}}+\sqrt{\frac{a}{x}}, \quad$ then $2 x y \frac{d y}{d x}$ is equal to

9Differentiation

If $x=a\left[\left\{\cos t+\frac{1}{2} \log \left(\tan ^2 \frac{t}{2}\right)\right\}\right]$ and $y=a \sin t$ then $\frac{d y}{d x}=$

10Differentiation

If $y=x+e^x$ then $\frac{d^2 x}{d y^2}=$

11Differentiation

Differentiate $\log _a x$ with respect to $a^x$

12Differentiation

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

13Differentiation

If $ 2 y=\left[\cot ^{-1}\left(\frac{\sqrt{3} \cos x+\sin x}{\cos x-\sqrt{3} \sin x}\right)\right]^2 \forall x \in\left(0, \frac{\pi}{2}\right)$ then $\frac{d y}{d x}$ is equal to :

14Differentiation

\(\text { If } \sin y=x(\cos (a+y)) \text {, then find } \frac{d y}{d x} \text { when } x=0\)

15Differentiation

If \(f(x)=f^{\prime}(x)\) and \(f(1)=2\), then \(f(3)\) is

16Differentiation

\(\text { If } y=\tan ^{-1}\left(\frac{3-2 x}{1+6 x}\right) \text { then } \frac{d y}{d x} \text { is }\)

17Differentiation

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

18Differentiation

\(\text { If } y=\sqrt{\sin x+y} \text { then find } \frac{d y}{d x} \text { at } x=0, \quad y=1\)

19Differentiation

\(\text { If } y=f(x), \quad p=\frac{d y}{d x} ; q=\frac{d^2 y}{d x^2} \text { then } \frac{d^2 x}{d y^2} \text { is equal to }\)

20Differentiation

\(\text { If } y=\sin ^{-1}\left(\frac{5 x+12 \sqrt{1-x^2}}{13}\right) \text { then } \frac{d y}{d x} \text { equals }\)

21Differentiation

\(\text { If } x^2+y^2=t+\frac{1}{t} \text { and } x^4+y^4=t^2+\frac{1}{t^2} \text { then } \frac{d y}{d x}=\)

22Differentiation

If \(f(x)=\frac{(x+1)^7 \sqrt{1+x^2}}{\left(x^2-x+1\right)^6}\) then the value of \(f^{\prime}(0)\) is equal to

23Differentiation

\(\text { If } f(x)=\sin ^{-1}\left(\frac{2^{x+1}}{1+4^x}\right) \text { then } f^{\prime}(0) \text { is equal to }\)

24Differentiation

The approximate value of \(f(5.001)\), where \(f(x)=x^3-7 x^2+10\)