What is the derivative of sin^3(x)cos(x)?

Jul 4, 2018

$\frac{d}{\mathrm{dx}} \left({\sin}^{3} x \cos x\right) = - {\sin}^{4} x + 3 {\sin}^{2} x {\cos}^{2} x$

Explanation:

Here We use: Product Rule , Power Rule and Differentiation of Trigonometric Functions

color(green)(d/dxsinx=cosx

color(green)(d/dxcosx=-sinx

$\frac{d}{\mathrm{dx}} \left({\sin}^{3} x \cos x\right) = {\sin}^{3} x \frac{d}{\mathrm{dx}} \left(\cos x\right) + \cos x \cdot 3 {\sin}^{2} x \frac{d}{\mathrm{dx}} \left(\sin x\right)$

$\frac{d}{\mathrm{dx}} \left({\sin}^{3} x \cos x\right) = {\sin}^{3} x \cdot \left(- \sin x\right) + 3 \cos x \cdot {\sin}^{2} x \cdot \cos x$

$\frac{d}{\mathrm{dx}} \left({\sin}^{3} x \cos x\right) = - {\sin}^{4} x + 3 {\sin}^{2} x {\cos}^{2} x$