Question

Ache as derivadas 1ª e 2ª de:
$f(x) = x^{3} \cos x$

Answer 1

f(x) = m(x).n(x)
f'(x) = m'(x).n(x) + n'(x).m(x)

f(x) = x³.cos x
f'(x) = (x³)'.cos x + (cos x)'.x³
f'(x) = 3x².cos x + (-sin x).x³
f'(x) = 3x².cos x - x³.sin x

f''(x) = (3x².cos x)' - (x³.sin x)'
f''(x) = [(3x²)'.cos x + (cos x)'.3x²] - [(x³)'.sin x + (sin x)'.x³
f''(x) = [6x.cos x + (-sin x).3x²] - [3x².sin x + cos x.x³]
f''(x) = 6x.cos x - 3x².sin x - 3x².sin x - x³.cos x
f''(x) = (6x - x³).cos x - 6x².sin x