Найдите производную функции 1 )sin2x-cos3x 2)5^x*sin x

Question

Найдите производную функции

1 )sin2x-cos3x

2)5^x*sin x

Answer 1

1) (Sin2x - Cos3x)' = (Sin2x)' - (Cos3x)' = Cos2x * (2x)' + Sin3x * (3x)' =
= 2Cos2x + 3Sin3x
2) (5^x * Sinx)' = (5^x)' * Sinx + 5^x * (Sinx)' = 5^x *ln5 * Sinx + 5^x * Cosx =
= 5^x(ln5 * Sinx + Cosx)