Question

найдите производную функции f(x)=4sin^5 2x

Answer 1

$f(x)=4\, sin^52x\\\\f'(x)=4\cdot 5\, sin^42x\cdot (sin2x)=20\, sin^42x\cdot cos2x\cdot (2x)'=\\\\=20\, sin^42x\cdot cos2x\cdot 2=40\cdot sin^42x\cdot cos2x$