# How do you differentiate Sin^3 x?

We have to find the derivative of sin3x

### Solution

To find the derivative of sin3x we will use the power rule.

Power rule states that if x is a variable and is raised to a power n, then the derivative of x raised to the power is represented by:

d/dx(xn) = nxn-1

$\frac{\mathrm{d} }{\mathrm{d} x} sin^{3}x= 3 \sin ^{2}x\frac{\mathrm{d} }{\mathrm{d} x}sin x$

We have learnt that d/dx (sin x) = cos x

Hence the above equation becomes

$\frac{\mathrm{d} }{\mathrm{d} x} sin^{3}x= 3 \sin ^{2}x\cos x$

$\frac{\mathrm{d} }{\mathrm{d} x} sin^{3}x= 3 \sin ^{2}x\cos x$