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1
TS EAMCET 2023 (Online) 12th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

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

A
$\sinh x$
B
$\cosh x$
C
$\tanh x$
D
$-\sinh x$
2
TS EAMCET 2023 (Online) 12th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

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

A
$-e^{-x}$
B
$e^x$
C
$x$
D
$y$
3
TS EAMCET 2023 (Online) 12th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $\tan y=\cot \left(\frac{\pi}{4}-x\right)$, then $\frac{d y}{d x}=$
A
$\frac{\operatorname{cosec}^2\left(\frac{\pi}{4}-x\right)}{1+\cot ^2\left(\frac{\pi}{4}+x\right)}$
B
$\frac{-\operatorname{cosec}^2\left(\frac{\pi}{4}-x\right)}{\sec ^2 y}$
C
$\frac{\operatorname{cosec}^2\left(\frac{\pi}{4}-x\right)}{1+\tan ^2\left(\frac{\pi}{4}+x\right)}$
D
$\frac{\sec ^2\left(\frac{\pi}{4}+x\right)}{1+\tan ^2\left(\frac{\pi}{4}+x\right)}$
4
TS EAMCET 2023 (Online) 12th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $x=3 \sqrt{2} \cos ^3 \theta$ and $y=4 \tan ^2 \theta$, then $\left(\frac{d y}{d x}\right)_{\theta=\pi / 4}=$
A
$\frac{32 \sqrt{2}}{9}$
B
$\frac{16}{9}$
C
$-\frac{16}{9}$
D
$-\frac{32}{9}$
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