1
TS EAMCET 2023 (Online) 14th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

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

A

$h(x)$

B

$\frac{1}{h(x)}$

C

$\log h(x)$

D

$-\log h(x)$

2
TS EAMCET 2023 (Online) 14th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

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

A

$\frac{3}{\sqrt{4-x^2}}$

B

$\frac{3}{\sqrt{1-x^2}}$

C

$\frac{1}{\sqrt{4-x^2}}$

D

$\frac{-1}{\sqrt{4-x^2}}$

3
TS EAMCET 2023 (Online) 13th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

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

A

$\frac{1}{2 \sqrt{\sqrt{\cosh (3)}}}\left(1+\frac{\sinh (3)}{\sqrt{\cosh (3)}}\right)$

B

$\frac{1}{2 \sqrt{\sqrt{\cosh (3)}}}\left(\log 3-\frac{\sinh (3)}{\sqrt{\cosh (3)}}\right)$

C

$\frac{\log 3 \sqrt{\cosh (3)}-\sinh (3)}{2(\cosh (3))^{\frac{3}{4}}}$

D

$\frac{\sqrt{\cosh (3)}-\sinh (3)}{2(\cosh (3))^{\frac{3}{4}}}$

4
TS EAMCET 2023 (Online) 13th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
  1. 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
A

$\frac{2}{9} \sqrt[3]{2}$

B

$\frac{\sqrt[3]{2}}{3}$

C

$\frac{4}{9} \sqrt[3]{2}$

D

$\frac{\sqrt[3]{2}}{9}$

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