First slide

Diffrentiation

Question

$y = x + x^{2} + \frac{1}{x} + \frac{1}{x^{3}} Find \frac{d y}{d x}$

Moderate

A

$1 + 2 x - \frac{1}{x^{2}} - \frac{3}{x^{4}}$
B

$1 + 2 x - \frac{1}{x^{2}} + \frac{2}{x^{4}}$
C

$1 - 2 x - \frac{1}{x^{2}} + \frac{3}{x^{4}}$
D

$1 + 2 x - \frac{1}{x^{2}} - \frac{3}{x^{3}}$

Solution

$\begin{array}{l} y = x + x^{2} + \frac{1}{x} + \frac{1}{x^{3}} \\ \frac{d y}{d x} = \frac{d x}{d x} + \frac{d x^{2}}{d x} + \frac{d x^{- 1}}{d x} + \frac{d x^{- 3}}{d x} \\ = 1 + 2 x + (- 1 x^{- 1 - 1}) + (- 3 x^{- 3 - 1}) (- \frac{d x}{d x} = 1, \frac{d x^{n}}{d x} = n x^{n - 1}) \\ = 1 + 2 x - \frac{1}{x^{2}} - \frac{3}{x^{4}} \end{array}$

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