The derivative of x+1x3 is - Infinity Learn by Sri Chaitanya

A
$3 x^{2} + \frac{3}{x^{4}} + 3 + \frac{3}{x^{2}}$
B
$3 x^{2} - \frac{3}{x^{4}} + 3 - \frac{3}{x^{2}}$
C
$3 x^{2} + \frac{3}{x^{4}} + 3 - \frac{3}{x^{2}}$
D
None of the above

Solution:

Let, ${(x + \frac{1}{x})}^{3}$

On differentiating w.r.t. r, we get

$\begin{matrix} \frac{dy}{dx} = \frac{d}{dx} {(x + \frac{1}{x})}^{3} \\ = \frac{d}{dx} \{x^{3} + \frac{1}{x^{3}} + 3 (x + \frac{1}{x})\} \end{matrix}$

$\begin{matrix} = \frac{d}{dx} (x^{3} + \frac{1}{x^{3}} + 3 x + \frac{3}{x}) \\ = 3 x^{2} - \frac{3}{x^{4}} + 3 - \frac{3}{x^{2}} \end{matrix}$

The derivative of ${(x + \frac{1}{x})}^{3}$ is

Solution:

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