Question

Найдите производную функции: f(x)=sin^5x+tg4x

Answer 1

$f(x)=Sin^{5}x+tg4x\\\\f'(x)=(Sin^{5}x)'+(tg4x)'=5Sin^{4} x*(Sinx)'+\frac{1}{Cos^{2}4x}*(4x)'=5Sin^{4}x Cosx+\frac{4}{Cos^{2}4x}\\\\Otvet:\boxed{5Sin^{4}x Cosx+\frac{4}{Cos^{2}4x}}$

Answer 2

$f'(x)=(\sin^5x+{\rm tg}\, 4x)'=5\sin^4x\cdot (\sin x)'+\dfrac{1}{\cos^24x}\cdot (4x)'=\\ \\ =5\sin^4x\cos x+\dfrac{4}{\cos^24x}$