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
\(\frac{\mathrm{d} }{\mathrm{d} x} sin^{3}x= 3 \sin ^{2}x\cos x\)Answer
\(\frac{\mathrm{d} }{\mathrm{d} x} sin^{3}x= 3 \sin ^{2}x\cos x\)
