sublimnoj7u7

2022-12-26

Derivative of $f\left(x\right)=4{e}^{x}-{4}^{x}+2\mathrm{ln}x$ is
A) $4{e}^{x}-{4}^{x}\mathrm{ln}4+\frac{2}{x}$
B) $4{e}^{x}+{4}^{x}\mathrm{ln}4+\frac{2}{x}$
C) $4{e}^{x}-{4}^{x}\mathrm{ln}4-\frac{2}{x}$
D) $4{e}^{x}-{4}^{x}\mathrm{ln}4+2x$

sobrevenilac

Expert

The correct answer is A) $4{e}^{x}-{4}^{x}\mathrm{ln}4+\frac{2}{x}$
As we know, $f\left(x\right)=4{e}^{x}-{4}^{x}+2\mathrm{ln}x$
Thus, derivative is given as
$\frac{df\left(x\right)}{dx}=\frac{d\left(4{e}^{x}-{4}^{x}+2\mathrm{ln}x\right)}{dx}$
$⇒4\frac{d{e}^{x}}{dx}-\frac{d{4}^{x}}{dx}+2\frac{d\left(\mathrm{ln}x\right)}{dx}$
$⇒4{e}^{x}-{4}^{x}\mathrm{ln}4+\frac{2}{x}$

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