1
AP EAPCET 2025 - 21st May Morning Shift
MCQ (Single Correct Answer)
+1
-0

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

A

14

B

$\frac{7}{8}$

C

1

D

7

2
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $y=\sinh ^{-1}\left(\frac{1-x}{1+x}\right)$, then $\frac{d y}{d x}$ is equal to
A
$\frac{-\sqrt{2}}{|1+x| \sqrt{1+x^2}}$
B
$\frac{-1}{(1+x) \sqrt{x}}$
C
$\frac{1}{\left(1+x^2\right) \sqrt{1+x}}$
D
$\frac{-\sqrt{2}}{(1+x) \sqrt{1-x}}$
3
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
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
A
-30
B
30
C
52
D
-52
4
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
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
A
$8 x y^{\prime}$
B
$-8 x\left(1+4 x^2\right) y^{\prime}$
C
$8 x\left(1+4 x^2\right) y^{\prime}$
D
$-8 x y^{\prime}$

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