Use the quotient rule to find the derivative?

f(x)=((4x-1)(3x^2+1))/(5x+2)

1 Answer
Mar 8, 2018

d/dx(g(x)/(h(x))) = (g'(x)*h(x) - h'(x)*g(x))/(h^2(x))

Explanation:

Using the quotient rule,
we get g(x) = (4x-1)(3x^2+1) and h(x) = 5x+2

g'(x) = 4(3x^2+1) + 6x(4x-1)
h'(x) = 5

d/dxf(x) = ((4(3x^2+1) + 6x(4x-1))(5x+2) - 5(4x-1)(3x^2+1))/(5x+2)^2

=> (120 x^3 + 57 x^2 - 12 x + 13)/(5 x + 2)^2