Evaluate `d/dx(sin^nx.cos^(n-1)x)`

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(d)/(dx)(sin{2cos^(-1)(sinx)}]=

(d)/(dx)(sin^(2)x+cos^(2)x) =

(d)/(dx)sin x

(d)/(dx)(sin^(-1)x+cos^(-1)x) is equal to

(d)/(dx)[3(sin^(2)x+cos^(2)x)]=

(d)/(dx)(e^(sin^(-1)x+cos^(-1)x))= ..........., (|x|<1)

(d)/(dx)cos^(-1)(sin x)=

d/(dx) (sin x+ cos x)

d/dx (e^(sin√x))

(d)/(dx)sin^(2)x