Question

Derivative of $f\left(x\right)=4e^x-4^x+2\ln x$ is

• A. $4e^x-4^x\ln 4+\frac{2}{x}$
• B. $4e^x+4^x\ln 4+\frac{2}{x}$
• C. $4e^x-4^x\ln 4-\frac{2}{x}$
• D. $4e^x-4^x\ln 4+2x$

Answer 1

The correct option is A $4e^x-4^x\ln 4+\frac{2}{x}$

Given, $f\left(x\right)=4e^x-4^x+2\ln x$
So, derivative is given as
$\frac{df\left(x\right)}{dx}=\frac{d(4e^x-4^x+2\ln x)}{dx}$
$\Rightarrow 4\frac{d{e}^x}{dx}-\frac{d{4}^x}{dx}+2\frac{d\left(\ln x\right)}{dx}$
$\Rightarrow 4e^x-4^x\ln 4+\frac{2}{x}$