Question

derivatives of 5sin³x+³​

Answer 1

$\rm{\displaystyle \frac{d}{dx}\left(5^{\sin ^3\left(x\right)+3}\right)}$

$\rm{\displaystyle =\frac{d}{dx}\left(e^{\left(\sin ^3\left(x\right)+3\right)\ln \left(5\right)}\right)}$

$\rm{\displaystyle =e^{\left(\sin ^3\left(x\right)+3\right)\ln \left(5\right)}\frac{d}{dx}\left(\left(\sin ^3\left(x\right)+3\right)\ln \left(5\right)\right)}$

$\rm{\displaystyle =e^{\left(\sin ^3\left(x\right)+3\right)\ln \left(5\right)}\cdot \:3\ln \left(5\right)\sin ^2\left(x\right)\cos \left(x\right)}$

$\rm{\displaystyle =3\ln \left(5\right)\cdot \:5^{\sin ^3\left(x\right)+3}\sin ^2\left(x\right)\cos \left(x\right)}$