# How do you find the derivative of (3x-2)^10 * (5x^2-x+1)^12?

May 14, 2015

In this way:

$y ' = \left[10 {\left(3 x - 2\right)}^{9} \cdot 3\right] \cdot {\left(5 {x}^{2} - x + 1\right)}^{12} +$

$+ {\left(3 x - 2\right)}^{10} \cdot \left[12 {\left(5 {x}^{2} - x + 1\right)}^{11} \cdot \left(10 x - 1\right)\right] =$

$= 6 {\left(3 x - 2\right)}^{9} {\left(5 {x}^{2} - x + 1\right)}^{11} \cdot \left[5 \left(5 {x}^{2} - x + 1\right) + 2 \left(3 x - 2\right) \left(10 x - 1\right)\right] =$

$= 6 {\left(3 x - 2\right)}^{9} {\left(5 {x}^{2} - x + 1\right)}^{11} \cdot \left(25 {x}^{2} - 5 x + 5 + 60 {x}^{2} - 6 x - 40 x + 4\right) =$

$= 6 {\left(3 x - 2\right)}^{9} {\left(5 {x}^{2} - x + 1\right)}^{11} \left(85 {x}^{2} - 51 x + 9\right) =$.