First slide

Derivatives

Question

$If f (x) = x - x^{2} + x^{3} - x^{4} + \dots \dots, | x | < 1, then f^{'} (x) =$

Moderate

A

$\frac{1}{1 + x}$
B

$\frac{1}{{(1 + x)}^{2}}$
C

$- \frac{1}{1 + x}$
D

$- \frac{1}{{(1 + x)}^{2}}$

Solution

$f (x) = \frac{x}{1 + x} \Rightarrow f' (x) = \frac{1}{{(1 + x)}^{2}}$

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