Question

Como calcular por derivada? f(x) = raiz x³ - 2x². Calcule f'(3)

Answer 1

f(x) = √(x³ - 2x²) =(x³-2x²)^(1/2)

f'(x) =(1/2)* (x³-2x²)^(1/2-1)  * ( 3x²-4x)

f'(x) =(1/2)* (x³-2x²)^(-1/2)  * ( 3x²-4x)

f'(x)= ( 3x²-4x)/[2*√(x³-2x²)]

f'(x)=x*(3x-4)/[2*√x²(x- 2)]

f'(x)=x*(3x-4)/[2x*√(x - 2)]

f'(3)=3*(3*3-4)/[2*3*√(3 - 2)]

f'(3)=3*5/6 =15/6