First slide

Derivatives

Question

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

Moderate

A

$\frac{1}{5}$
B

$\frac{1}{25}$
C

5
D

$\frac{1}{16}$

Solution

$f (x) = \frac{1}{1 + 1 / x} = \frac{x}{x + 1}, g (x) = \frac{1}{1 + 1 / f (x)} = \frac{1}{1 + (x + 1) / x} = \frac{x}{2 x + 1}$
$g' (x) = \frac{(2 x + 1) 1 - x (2)}{{(2 x + 1)}^{2}} = \frac{1}{{(2 x + 1)}^{2}} \Rightarrow g' (2) = \frac{1}{25} .$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App