Question

Obtenha a derivada:
f(x) = √x^5 / (x^3 - x)^5

Answer 1

Regra do quociente

d(f(x))/dx=5/2.x^3/2.(x^3-x^5)-5(x³-x)⁴.√x^5/[(x³-x)^5]²

Answer 2

Resposta:

f(x) = √x^5 / (x^3 - x)^5

f'(x)= [( √x^5)' *(x^3 - x)^5 - √x^5  * [(x^3 - x)^5]' ] /(x^3 - x)^10

f'(x)= [( (5/2)*x^(3/2)) *(x^3 - x)^5 - √x^5  * [5(x^3 - x)^4 *(3x²-1)] ] /(x^3 - x)^10