Question

Find the derivative of the following function
$f\left(x\right)=\sin \left(2x^2+4^x+3\right)$

• A. $-\cos (2x^2+4^x+3)\left(4x+4^x\ln 4\right)$
• B. $\cos (2x^2+4^x+3)\left(4x+4^x\ln 4\right)$
• C. $\cos (2x^2+4^x+3)\left(4x+4^x\right)$
• D. $-\cos (2x^2+4^x+3)\left(4x+4^x\right)$

Answer 1

The correct option is B $\cos (2x^2+4^x+3)\left(4x+4^x\ln 4\right)$

$f\left(x\right)=\sin (2x^2+4^x+3)$
$f\text{'}\left(x\right)=\frac{d\left(\sin (2x^2+4^x+3)\right)}{\mathrm{dx}}\times \frac{d\left(2x^2+4^x+3\right)}{\mathrm{dx}}$
$f\text{'}\left(x\right)=\cos (2x^2+4^x+3)\times \left(4x+4^x\ln \left(4\right)\right)$