Differentiation PYQs - Last 10 Years

AP EAPCET / Mathematics / Calculus / 60 recent questions

MathematicsCalculus2016-2025

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Practice 60 AP EAPCET 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 10 Years Differentiation Questions

Showing 50 of 60 filtered questions.

1Differentiation

If $(a+\sqrt{2} b \cos x)(a-\sqrt{2} b \cos y) =a^2-b^2$, where $a>b>0$, then at $\left(\frac{\pi}{4}, \frac{\pi}{4}\right), \frac{d y}{d x}=$

2Differentiation

If $x=\sqrt{2^{\operatorname{cosec}^{-1} t}}$ and $y=\sqrt{2^{\sec ^{-1} t}},|t| \geq 1$, then $\frac{d y}{d x}=$

3Differentiation

If $y=\left(\log _x \sin x\right)^x$, then $\frac{d y}{d x}=$

4Differentiation

If $\sin x \sqrt{\cos y}-\cos y \sqrt{\sin x}=0$, then $\frac{d y}{d x}=$

5Differentiation

If $f(x)=x^{\sec ^{-1} x}$, then $f^{\prime}(2)=$

6Differentiation

If $x^2+y^2+\sin y=4$, then the value of $\frac{d^2 y}{d x^2}$ at $x=-2$ is

7Differentiation

If $y=\sqrt{\frac{x^4 \sqrt{3 x-5}}{\left(x^2-3\right)(2 x-3)}}$, then $\left(\frac{d y}{d x}\right)_{x=2}=$

8Differentiation

If $y=\tan ^{-1}\left(\frac{3 x-x^3}{1-3 x^2}\right)+\tan ^{-1}\left(\frac{7 x}{1-12 x^2}\right)$, then at $x=0, \frac{d y}{d x}=$

9Differentiation

If $x=\sqrt{2} e^t(\sin t-\cos t)$ and $y=\sqrt{2} e^t(\sin t+\cos t)$, then $\left(\frac{d^2 y}{d x^2}\right)_{t=\frac{\pi}{4}}=$

10Differentiation

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

11Differentiation

If $y=\sqrt{\cosh x+\sqrt{\cosh x}}$, then $\frac{d y}{d x}=$

12Differentiation

If $y=(\log x)^{1 / x}+x^{\log x}$, at $x=e, \frac{d y}{d x}=$

13Differentiation

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

14Differentiation

Assertion (A) If $y=f(x)=(|x|-|x-1|)^2$, then $\left(\frac{d y}{d x}\right)_{x=1}=1$
Reason (R) $\mathop {\lim }\limits_{x \to a} \frac{f(x)-f(a)}{x-a}$ exist, then it is called derivative of $f(x)$ at $x=a$.

15Differentiation

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

16Differentiation

If $g$ is the inverse of the function $f(x)$ and $g(x)=x+\tan x$, then $f^{\prime}(x)=$

17Differentiation

If $y=(a x+b) \cos x$, then
\(y_2+y_1 \sin 2 x+y\left(1+\sin ^2 x\right)=\)

18Differentiation

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

19Differentiation

If $5 f(x)+3 f\left(\frac{1}{x}\right)=x+2$ and $y=x f(x)$, then $\frac{d y}{d x}$ at $x=1$ is equal to

20Differentiation

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

21Differentiation

If $y=\left(\tan ^{-1} 2 x\right)^2+\left(\cot ^{-1} 2 x\right)^2$, then $\left(1+4 x^2\right)^2 y^{\prime \prime}-16$ is equal to

22Differentiation

If $y=(x-1)(x+2)\left(x^2+5\right)\left(x^4+8\right)$, then $\lim _{x \rightarrow-1}\left(\frac{d y}{d x}\right)$ is equal to

23Differentiation

64. If $f(0)=0, f^{\prime}(0)=3$, then the derivative of $y=f(f(f(f(f(x)))))$ at $x=0$ is

24Differentiation

If $y=\sqrt{\sin x+\sqrt{\sin x+\sqrt{\sin x+\ldots \infty}}}$, then the value of $\frac{d^2 y}{d x^2}$ at the point $(\pi, 1)$ is

25Differentiation

If $y=1+x+x^2+x^3+\ldots \ldots \infty$ and $|x|<1$, then $y^{\prime \prime}$ is equal to

26Differentiation

If $y=\tan ^{-1} \frac{x}{1+2 x^2}+\tan ^{-1} \frac{x}{1+6 x^2}+\tan ^{-1} \frac{x}{1+12 x^2}$, then $\left(\frac{d y}{d x}\right)_{x=\frac{1}{2}}$ is equal to

27Differentiation

If $f(x)=5 \cos ^3 x-3 \sin ^2 x$ and $g(x)=4 \sin ^3 x+\cos ^2 x$, then the derivative of $f(x)$ with respect to $g(x)$ is

28Differentiation

Which one of the following is false ?

29Differentiation

The rate of change of $x^{\sin x}$ with respect to $(\sin x)^x$ is

30Differentiation

If $y=\frac{\alpha x+\beta}{\gamma \alpha+\delta}$, then $2 y_1 y_3=$

31Differentiation

If $\frac{d}{d x}\left(\frac{1+x^2+x^4}{1+x+x^2}\right)=a x+b$, then $(a, b)=$

32Differentiation

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

33Differentiation

If $y=x-x^2$, then the rate of change of $y^2$ with respect to $x^2$ at $x=2$ is

34Differentiation

For $x<0, \frac{d}{d x}\left[|x|^x\right]=$

35Differentiation

If $y=t^2+t^3$ and $x=t-t^4$, then $\frac{d^2 y}{d x^2}$ at $t=1$ is

36Differentiation

If $y=f(x)$ is a thrice differentiable function and a bijection, then $\frac{d^2 x}{d y^2}\left(\frac{d y}{d x}\right)^3+\frac{d^2 y}{d x^2}=$

37Differentiation

The length of the tangent drawn at the point $P\left(\frac{\pi}{4}\right)$ on the curve $x^{2 / 3}+y^{2 / 3}=2^{2 / 3}$ is

38Differentiation

If $x=3\left[\sin t-\log \left(\cot \frac{t}{2}\right)\right]$ and $y=6\left[\cos t+\log \left(\operatorname{tin} \frac{t}{2}\right)\right]$ then $\frac{d y}{d x}=$

39Differentiation

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

40Differentiation

If $y=\frac{\log x}{x}$, then the value of $x^2 \frac{d^2 y}{d x^2}+3 x \frac{d y}{d x}+y$ at the point $(\sqrt[3]{e}, \sqrt{e})$ is

41Differentiation

If $f(x)=|x-5|+|x+5|+|x-4|+|x+4|$, then $\frac{f^{\prime}(1)-f^{\prime}(-6)}{f^{\prime}(-1)+f^{\prime}(6)}=$

42Differentiation

If $x^x y^y=e^e$, then $\left(\frac{d^2 y}{d x^2}\right)_{(e, e)}=$

43Differentiation

If $f(x+a y)+g(x-a y)=0$, then $a \frac{d y}{d x}=$

44Differentiation

\(y=x^3-a x^2+48 x+7\) is an increasing function for all real values of \(x\), then \(a\) lies in the interval

45Differentiation

If \(x=f(\theta)\) and \(y=g(\theta)\), then \(\frac{d^2 y}{d x^2}=\)

46Differentiation

Assertion (A) \(\frac{d}{d x}\left(\frac{x^2 \sin x}{\log x}\right)=\frac{x^2 \sin x}{\log x}\left(\cot x+\frac{2}{x}-\frac{1}{x \log x}\right)\)
Reason (R) $$\frac{d}{d x}\left(\frac{u v}{w}\right)=\frac{u v}{w}\left[\frac{u^{\prime}}{u}+\...

47Differentiation

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

48Differentiation

If \(x \neq 0\) and \(f(x)\) satisfies \(8 f(x)+6 f(1 / x) =x+5\), then \(\frac{d}{d x}\left(x^2 f(x)\right)\) at \(x=1\) is

49Differentiation

If \(y=\left(1+\frac{1}{x}\right)\left(1+\frac{2}{x}\right)\left(1+\frac{3}{x}\right) \ldots\left(1+\frac{n}{x}\right)\) and \(x \neq 0\). When \(x=-1, \frac{d y}{d x}\) is equal to

50Differentiation

If \(f(x)=2x^2+3x-5\), then the value of \(f'(0)+3f'(-1)\) is equal to