Question

Find derivative of $f\left(x\right)=e^{\sin x}+\ln x+8^x$

• A. $\cos x{e}^{\sin x}+\frac{1}{x}+8^x\ln x$
• B. $\cos x{e}^{\sin x}+\frac{1}{x}+8^x\ln 8$
• C. $\sin x{e}^{\sin x}+\frac{1}{x}+8^x\ln 8$
• D. $\cos x{e}^{\cos x}+\frac{1}{x}+8^x\ln x$

Answer 1

The correct option is B $\cos x{e}^{\sin x}+\frac{1}{x}+8^x\ln 8$

Given: $f\left(x\right)=e^{\sin x}+\ln x+8^x$
$f^{{}^{\prime }}\left(x\right)=\frac{d{e}^{\sin x}}{dx}+\frac{d\ln x}{dx}+\frac{d{8}^x}{dx}$
$\Rightarrow \frac{d{e}^{\sin x}}{d\sin x}\times \frac{d\sin x}{dx}+\frac{1}{x}+8^x\ln 8$
$\Rightarrow f^{{}^{\prime }}\left(x\right)=\cos x.e^{\sin x}+\frac{1}{x}+8^x\ln 8$