Question

Derivada de 2x + 3x² - 4/x

Answer 1

Regra do quociente:

(f/g)' = f' * g - f * g' / g²

f(x) = 2x + 3x² - 4 ⇒ f'(x) = 2 + 6x 

g(x) = x ⇒ g'(x) = 1

(f/g)' = (2 +6x) * x - (2x + 3x² -4) / x²

(f/g)' = 2x + 6x² - 2x - 3x² +4 / x²

(f/g)' =  (4 + 3x²) / x²

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17/02/2016 
Sepauto - SSRC
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Answer 2

Vamos usar a regra do quociente:

$\large\boxed{(\frac{u}{v})'=\frac{u'\cdot~v-u\cdot~v'}{v^2}}$

Então, temos que:

$f(x)=\frac{2x+3x^2-4}{x}\\ \\ f'(x)=\frac{(2+6x)\cdot~x-(2x+3x^2-4)\cdot~1}{x^2}\\ \\ f'(x)=\frac{2x+6x^2-2x-3x^2+4}{x^2}\\ \\ \large\boxed{f'(x)=\frac{3x^2+4}{x^2}}$