70
MCQ (Single Correct Answer)
If $y=\frac{1+\frac{1}{x^2}}{1-\frac{1}{x^2}}$, then $\frac{d y}{d x}$ is equal to
A
$\frac{-4 x}{\left(x^2-1\right)^2}$
B
$\frac{-4 x}{x^2-1}$
C
$\frac{1-x^2}{4 x}$
D
$\frac{4 x}{x^2-1}$
71
MCQ (Single Correct Answer)
If $y=\frac{\sin x+\cos x}{\sin x-\cos x}$, then $\frac{d y}{d x}$ at $x=0$ is equal to
A
$-$2
B
0
C
$\frac{1}{2}$
D
Does not exist
72
MCQ (Single Correct Answer)
If $y=\frac{\sin (x+9)}{\cos x}$, then $\frac{d y}{d x}$ at $x=0$ is equal to
A
$\cos9$
B
$\sin9$
C
0
D
1
73
MCQ (Single Correct Answer)
If $f(x)=1+x+\frac{x^2}{2}+\ldots+\frac{x^{100}}{100}$, then $f^{\prime}(1)$ is equal to
A
$\frac{1}{100}$
B
100
C
0
D
Does not exist
74
MCQ (Single Correct Answer)
If $f(x)=\frac{x^n-a^n}{x-a}$ for some constant $a$, then $f^{\prime}(a)$ is equal to
A
1
B
0
C
$\frac{1}{2}$
D
Does not exist