Question

Encontrar a DERIVADA da função abaixo:

$f( x})= \frac{x^{4}}{x^{2}} + \frac{2}{x^{6}}$

Answer 1

$f'(x) = \frac{4.x^{4-1} \ . \ x^2 \ - \ (x^4 \ . \ 2.x^{2-1})}{(x^2)^2} \ + \ \frac{0 \ . \ x^6 \ - \ (2 \ . \ 6.x^{6-1})}{(x^6)^2}$

$f'(x) = \frac{4x^3 \ . \ x^2 \ - \ (x^4 \ . \ 2x)}{x^4} \ + \ \frac{0 \ - \ (2 \ . \ 6x^5)}{x^{12}}$

$f'(x) = \frac{4x^5 \ - \ 2x^5}{x^4} \ - \ \frac{12x^5}{x^{12}}$

$f'(x) = \frac{2x^5}{x^4} \ - \ \frac{12x^5}{x^{12}}$

2x - 12x⁻⁷ = $2x \ - \ \frac{1}{12x^7}$

Answer 2

f(x) = x⁴/x² + 2/x⁶ = x² + 2x⁻⁶ ⇒ f(x)' = 2x - 12x⁻⁷ = 2x - 12/x⁷