Find derivatives of e ^ 2 x - x - Vidyadip

Question

Find derivatives of $e ^{2 x }-\tan x$

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Answer

Using $\frac{d}{d x}\left[f_1(x)-f_2(x)\right]=\frac{d f_1(x)}{d x}-\frac{d f_2(x)}{d x}$
Here, $f _1( x )= e ^{2 x }$ and $f _2( x )=\tan x$
$\begin{aligned} \therefore \quad \frac{d}{d x}\left(e^{2 x}-\tan x\right) & =\frac{d\left(e^{2 x}\right)}{d x}-\frac{d(\tan x)}{d x} \\ & =2 e^{2 x}-\sec ^2 x\end{aligned}$

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