Question

Qual a derivada de f(x)=x^4/3+2/x^2?

Answer 1

f(x)=x⁴/3+2/x²

f(x)=x^6+6/3x²

regra do quociente

f'(x)=(3x²).(x^6+6)'-(x^6+6).(3x²)'/(3x²)²
f'(x)=(3x²)(6x^5)-(x^6+6).(6x)/9x⁴
f'(x)=18x^7-6x(x^6+6)/9x⁴

$\boxed{ \mathsf{ \frac{df(x)}{x} = \frac{ {18x}^{7} - 6x( {x}^{6} + 6 ) }{ {9x}^{4} } }}$

Answer 2

f(x)=x^4/3+2/x^2


mmc:

3,x^2/x
3,x/x
3,1/3
1,1/

mmc=>3x^2

f(x)=x^2.x^4/3x^2+3.2/3x^2


f(x)=x^6+6

f(x)'=6x^(6-1)

_______
f(x)'=6x^5

espero ter ajudado!

boa tarde!