1
AP EAPCET 2024 - 22th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

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

A
$\frac{5 \cos +2}{6 \cos x-1}$
B
$-\left(\frac{5 \cos x+2}{6 \cos x-1}\right)$
C
$\frac{15 \cos x-6}{12 \sin x+2}$
D
$-\left(\frac{15 \cos x+6}{12 \sin x-2}\right)$
2
AP EAPCET 2024 - 22th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $y=1+x+x^2+x^3+\ldots \ldots \infty$ and $|x|<1$, then $y^{\prime \prime}$ is equal to
A
$2 y^{\prime}$
B
$\frac{2 y}{y^{\prime}}$
C
$\frac{y^{\prime}}{2 y}$
D
$2 y^2 y^{\prime}$
3
AP EAPCET 2024 - 22th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

    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

A
2
B
-2
C
$-\frac{1}{2}$
D
$\frac{1}{2}$
4
AP EAPCET 2024 - 22th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
64. If $f(0)=0, f^{\prime}(0)=3$, then the derivative of $y=f(f(f(f(f(x)))))$ at $x=0$ is
A
16
B
32
C
81
D
243
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