Find the derivative of the following w.r.t x:

1)sin²x 2)sin^mx cosⁿx

1) d/dx (sin²x) = 2sinx . d/dx (sinx)= -2sinxcosx

2) d/dx(sin^mxcosⁿx)= cosⁿx. d/dx (sin^mx) + sin^mx . d/dx (cosⁿx)= mcosⁿx .sin^m-1x (cosx) - nsin^mxcos^n-1x (sinx)

=mcosⁿ⁺¹xsin^m-1x -- nsin^m+1xcos^n-1x = cos^n-1xsin^m-1x(mcos²x -- nsin²x)