Question

How do you differentiate `f(x)=((3x+4)/(6x+7))^3` using the quotient rule?

Answer 1

`f'(x) = -9 * (3x + 4)^2 cdot (6x + 7)^-4`

Explanation:

`(df) / dx = 3 cdot (frac{3x + 4}{6x + 7})^2 cdot d/dx u/v`

`u = 3x + 4 Rightarrow u' = 3`

`v = 6x + 7 Rightarrow v' = 6`

`(df) / dx = 3 cdot (frac{3x + 4}{6x + 7})^2 cdot (3 (6x + 7) - (3x + 4) 6)/(6x + 7)^2`

`(df) / dx = 3 cdot (frac{3x + 4}{6x + 7})^2 cdot (-3)/(6x + 7)^2`