Differentiation PYQs - Last 10 Years

TS EAMCET / Mathematics / Calculus / 79 recent questions

MathematicsCalculus2016-2025

All Differentiation PYQs Last 5 Years Create chapter test

Practice 79 TS EAMCET 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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2020-2025

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64 in last 5 years79 in last 10 years

Last 10 Years Differentiation Questions

Showing 50 of 79 filtered questions.

1Differentiation

If $y=x^{\log x}+(\log x)^x, x>1$, then $\left(\frac{d y}{d x}\right)_{x=e}=$

2Differentiation

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

3Differentiation

If $x=t-\sin t, y=1-\cos t$ and $\frac{d^2 y}{d x^2}=-1$ at $t=k, k>0$ then $\lim _{i \rightarrow K} \frac{y}{x}=$

4Differentiation

If $f(x)=\log _{\left(x^2-2 x+1\right)}\left(x^2-3 x+2\right), x \in R-[1,2]$ and $x \neq 0$, then $f^{\prime}(3)=$

5Differentiation

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

6Differentiation

If $3^x y^x=x^{3 y}$, then the value of $\frac{d y}{d x}$ at $x=1$ is

7Differentiation

If $y=\sqrt{\log \left(x^2+1\right)+\sqrt{\log \left(x^2+1\right)+\sqrt{\log \left(x^2+1\right)+\ldots+\infty}}, \text {, } 100.00}$, $|x|<1$, then $\frac{d y}{d x}=$

8Differentiation

If $x=\sin 2 \theta \cos 3 \theta, y=\sin 3 \theta \cos 2 \theta$, then $\frac{d y}{d x}=$

9Differentiation

If $x=\sqrt{1-\tan y}$, then $\frac{d y}{d x}=$

10Differentiation

If $x=\frac{t^2}{1+t^5}, y=\frac{2 t^3}{1+t^5}$ and $t \neq-1$ is a perimeter, then $\frac{d y}{d x}=$

11Differentiation

If $\left(x^2-3 x+2\right)^{\frac{y}{x^{2-1}}}=x+2$, then $\left(\frac{d y}{d x}\right)_{x=0}=$

12Differentiation

If $y=f(\cosh x)$ and $f^{\prime}(x)=\log \left(x+\sqrt{x^2-1}\right)$, then $\frac{d^2 y}{d x^2}=$

13Differentiation

If $\frac{d}{d x}\left\{\left(\frac{x-1}{x-\sqrt{x}}\right) e^{2 x+1}\right\}=\frac{x-1}{x-\sqrt{x}} e^{2 x+1} f(x)$, then $f(4)=$

14Differentiation

If $2 x^2-3 x y+4 y^2+2 x-3 y+4=0$, then $\left(\frac{d y}{d x}\right)_{(3,2)}=$

15Differentiation

If $y=\sin a x+\cos b x$, then $y^{\prime \prime}+b^2 y=$

16Differentiation

If $x=\frac{9 t^2}{1+t^4}$ and $y=\frac{16 t^2}{1-t^4}$ then $\frac{d y}{d x}=$

17Differentiation

A particle moving from a fixed point on a straight line travels a distance $S$ metres in $t \mathrm{sec}$. If $S=t^3-t^2-t+3$, then the distance (in mts) travelled by the particle when it comes to rest, is

18Differentiation

If $y=44 x^{45}+45 x^{-44}$, then $y^n=$

19Differentiation

If $y(\cos x)^{\sin x}=(\sin x)^{\sin x}$, then the value of $\frac{d y}{d x}$ at $x=\frac{\pi}{4}$ is

20Differentiation

If $y=\frac{\tan x \cos ^{-1} x}{\sqrt{1-x^2}}$, then the value of $\frac{d y}{d x}$, when $x=0$ is

21Differentiation

If $y=\sqrt{\sin (\log 2 x)+\sqrt{\sin (\log 2 x)+\sqrt{\sin (\log 2 x)+\ldots \infty,}}}$ then $\frac{d y}{d x}=$

22Differentiation

Derivative of $(\sin x)^{x}$ with respect to $x^{(\sin x)}$ is

23Differentiation

A function $f: R \rightarrow R$ is such that $y f(x+y)+\cos m x y=1+y f(x)$. If $m=2$, then $f^{\prime}(x)=$

24Differentiation

If $y=\tan ^{-1}\left[\frac{\sin ^{3}(2 x)-3 x^{2} \sin (2 x)}{3 x \sin ^{2}(2 x)-x^{3}}\right]$, then $\frac{d y}{d x}=$

25Differentiation

If $y=\log \left[\tan \sqrt{\frac{2^x-1}{2^x+1}}\right], x>0$, then $\left(\frac{d y}{d x}\right)_{x=1}=$

26Differentiation

If $\log y=y^{\log x}$, then $\frac{d y}{d x}=$

27Differentiation

If $y=a \cos 3 x+b e^{-x}$, then $y^{\prime \prime}(3 \sin 3 x-\cos 3 x)=$

28Differentiation

If $y=\log \left(x-\sqrt{x^{2}-1}\right)$, then $\left(x^{2}-1\right) y^{\prime \prime}+x y^{\prime}+e^{y}+\sqrt{x^{2}-1}=$

29Differentiation

On differentiation if we get $f(x, y) d y-g(x, y) d x=0$ from $2 x^2-3 x y+y^2+x+2 y-8=0$, then $\frac{g(2,2)}{f(1,1)}=$

30Differentiation

If $f(x)=e^x, h(x)=(f \circ f)(x)$, then $\frac{h^{\prime}(x)}{h(x)}=$

31Differentiation

If $\sin y=\sin 3 t$ and $x=\sin t$, then $\frac{d y}{d x}=$

32Differentiation

If $f(x)=\sqrt{x}(x \geq 0)$ and $g(x)=1+x^2$, then $(f \circ g)^{\prime}(1)=$

33Differentiation

If $y=x \sin x$ and $\frac{\frac{d y}{d x}-\frac{y}{x}}{x \frac{d y}{d x}-y}$ at $x=\alpha$ is 1 , then $\alpha=$

34Differentiation

Match the values of $\frac{d y}{d x}$ at $x=\frac{\pi}{3}$ for the following system of curves in parametric form given in List-I with those of the items in List-II

List-I
List-II

(i)

x
=
a
(
θ
−
sin
⁡
θ
)
,
y
...

35Differentiation

If $f(x)=|x-1|+|x-2|$, then
\(f^{\prime}(-2023)+f^{\prime}\left(\frac{2024}{2023}\right)+f^{\prime}(2023)=\)

36Differentiation

If $f(x)=x^{\tan x}+(\tan x)^x$, then $f^{\prime}\left(\frac{\pi}{4}\right)=$

37Differentiation

If $f(x)=\frac{e^{2 x}-e^{-2 x}}{e^{3 x}+e^{-3 x}}$, then $f^{\prime}(0)=$

38Differentiation

If $2 x^2+3 x y-y^2+4 x-5 y+6=0$, then the value of $\frac{d y}{d x}$ at $(x, y)=(1,-2)$ is

39Differentiation

If $x=\cos ^3 \theta-\sin ^3 \theta$ and $y=\sqrt[3]{\cos \theta}-\sqrt[3]{\sin \theta}$, then the value of $\frac{d y}{d x}$ at $\theta=\frac{\pi}{4}$ is

40Differentiation

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

41Differentiation

If $x=3 \sqrt{2} \cos ^3 \theta$ and $y=4 \tan ^2 \theta$, then $\left(\frac{d y}{d x}\right)_{\theta=\pi / 4}=$

42Differentiation

If the slope of the tangent drawn to the curve $y=e^{a+b x^2}$ at the point $P(1,1)$ is -2 , then the value of $2 a-3 b$ is

43Differentiation

If $\tan y=\cot \left(\frac{\pi}{4}-x\right)$, then $\frac{d y}{d x}=$

44Differentiation

The derivative of $\frac{1-x^2}{1+x^2}$ with respect to $\frac{2 x}{1+x^2}$ at $x=2$ is

45Differentiation

If $x=\log p$ and $y=\frac{1}{p}$, then $\frac{d y}{d x}=$

46Differentiation

If $e^x=y+\sqrt{y^2-1}$, then $\frac{d y}{d x}=$

47Differentiation

If $\sec \left(\log _2 y^2\right)=\operatorname{cosec}\left(\log _2 x^2\right)$, then $\frac{d y}{d x}=$

48Differentiation

If $y=\frac{e^{\sin x}+\sinh ^3 x}{\cosh x-\tan x}$, then $y^{\prime}(0)=$

49Differentiation

If $f(x)=\frac{e^{-x} \sin x}{\log _e x}$ and $f^{\prime}(x)=f(x) \cdot g(x)$, then $g^{\prime}(e)=$

50Differentiation

If $y=\frac{a x+b}{c x+d}$, then $\frac{d x}{d y}=$