Question

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

Answer 1

In this way:

`y'=[10(3x-2)^9*3] * (5x^2-x+1)^12+`

`+(3x-2)^10*[12(5x^2-x+1)^11*(10x-1)]=`

`=6(3x-2)^9(5x^2-x+1)^11 * [5(5x^2-x+1)+2(3x-2)(10x-1)]=`

`=6(3x-2)^9(5x^2-x+1)^11 * (25x^2-5x+5+60x^2-6x-40x+4)=`

`=6(3x-2)^9(5x^2-x+1)^11(85x^2-51x+9)=`.