# How do you differentiate y = (2x+3)^4 / x?

Jun 25, 2015

$y ' = \frac{3 {\left(2 x + 3\right)}^{3} \left[2 x - 1\right]}{x} ^ 2$
I would use the Quotient and Chain Rule (this last one to deal with ${\left(\right)}^{4}$):
$y ' = \frac{4 {\left(2 x + 3\right)}^{3} \cdot 2 \cdot x - {\left(2 x + 3\right)}^{4} \cdot 1}{x} ^ 2 =$
$= \frac{{\left(2 x + 3\right)}^{3} \left[8 x - 2 x - 3\right]}{x} ^ 2 = \frac{{\left(2 x + 3\right)}^{3} \left[6 x - 3\right]}{x} ^ 2 =$
$= \frac{3 {\left(2 x + 3\right)}^{3} \left[2 x - 1\right]}{x} ^ 2$