Question

Dada a função de ƒ(x) = x2 - e2x, a alternativa que representa a 3ª derivada é

Answer 1

$f'(x)=2x^1-(e^{2x})'\\\\\\f'(x)=2x^1-2\cdot e^{2x}\\\\\\f'(x)=2x-2\cdot e^{2x}\\\\\\\\f''(x) = (2x-2\cdot e^{2x})'\\\\\\f''(x) = 2-2\cdot (e^{2x})'\\\\\\f''(x) = 2-2\cdot 2\cdot e^{2x}\\\\\\f''(x) = 2-4\cdot e^{2x}$

$f'''(x) = (2-4\cdot e^{2x})'\\\\\\f'''(x) = 0-4\cdot (e^{2x})'\\\\\\f'''(x) = 0-4\cdot 2\cdot e^{2x}\\\\\\f'''(x) = -8\cdot e^{2x}$