How do you find the derivative of y = (2x+3)^4 / x?

Feb 28, 2016

$\frac{{\left(2 x + 3\right)}^{3} \left(8 {x}^{2} - 2 x - 3\right)}{x} ^ 2$

Explanation:

By applying the quotient rule, the derivative would be

$\frac{4 {\left(2 x + 3\right)}^{3} \left(2 x\right) \left(x\right) - {\left(2 x + 3\right)}^{4}}{x} ^ 2$

=$\frac{{\left(2 x + 3\right)}^{3} \left(8 {x}^{2} - 2 x - 3\right)}{x} ^ 2$

Feb 28, 2016

$\frac{\left[8 x \cdot {\left(2 x + 3\right)}^{3}\right] - \left[{\left(2 x + 3\right)}^{4}\right]}{x} ^ 2$

Explanation:

Using quotient rule,

$\frac{d}{\mathrm{dx}} {\left(2 x + 3\right)}^{4} / x = \frac{\left[8 x \cdot {\left(2 x + 3\right)}^{3}\right] - \left[{\left(2 x + 3\right)}^{4}\right]}{x} ^ 2$