Differentiati… | NUST Entrance Test Mathematics

IF $f(x)=\frac{ax+b}{cx+d}$ then f'(0) equals:

Difficulty: Easy

A:

bc-ad

B:

\frac{ad+bc}{d^{2}}

C:

\frac{ad-bc}{d^{2}}

D:

b/d

If $y=x^{-3}+2x^{-\frac{3}{2}}+3$, then dy/dx equals:

Difficulty: Easy

A:

\frac{x^{4}}{x^{\frac{5}{2}}}

B:

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

C:

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

D:

x^{-4}-x^{-\frac{5}{2}}

$\frac{\text{d}}{\text{d}x}(\sqrt{x} -\frac{1}{\sqrt{x}})^{2}$=

Difficulty: Easy

A:

2x^{2}-1

B:

1-x^{2}

C:

\frac{x^{2}-1}{x^{2}}

D:

1+x^{2}

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