# How do you differentiate p(y) = (y + ln(y)y^2(5y^3 + 9y^4) using the product rule?

Feb 29, 2016

$1 + \ln \left(y\right) \left(25 {y}^{4} + 54 {y}^{5}\right) + \left(5 {y}^{4} + 9 {y}^{5}\right)$

#### Explanation:

Write$p \left(y\right) = y + \ln \left(y\right) \cdot \left(5 {y}^{5} + 9 {y}^{6}\right)$

$p ' \left(y\right) = 1 + \ln \left(y\right) \left(25 {y}^{4} + 54 {y}^{5}\right) + \left(\frac{1}{y}\right) \left(5 {y}^{5} + 9 {y}^{6}\right)$

=$1 + \ln \left(y\right) \left(25 {y}^{4} + 54 {y}^{5}\right) + \left(5 {y}^{4} + 9 {y}^{5}\right)$