y=x+x2+1x+1x3 Find dydx - Sri Chaitanya Infinity Learn Best Online Courses for NCERT Solutions, CBSE, ICSE, JEE, NEET, Olympiad and Class 6 to 12

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:

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

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

Solution:

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