Differentiate the following w.r.t. x : y= x+ x-x^3 - Vidyadip

Question

Differentiate the following w.r.t. x :

$y=\sqrt{ } x+\tan x-x^3$

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Answer

$y=\sqrt{x}+\tan x-x^3$
Differentiating w.r.t. $x$, we get
$\begin{aligned}
\frac{ d y}{ d x} & =\frac{ d }{ d x}\left(\sqrt{x}+\tan x-x^3\right) \\
\frac{ d y}{ d x} & =\frac{ d }{ d x}(\sqrt{x})+\frac{ d }{ d x}(\tan x)-\frac{ d }{ d x}\left(x^3\right) \\
& =\frac{1}{2 \sqrt{x}}+\sec ^2 x-3 x^2
\end{aligned}$

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