Производная y=3sinxcos^4*x

Question

Производная y=3sinxcos^4*x

Answer 1

у ′ = 3(sin ′ x cos^4* x+sin x (cos^4 *x ) ′ )=3 cos x cos^4 *x+sinx*4cos^3x*
*(-sin x)= 3(cos^5 *x-4 sin^2x cos^3 x= 3 cos^3 x(cos^2 x-4sin^2 x)