Hello This problem, wants me to take the derviative of y=x^6(3x-2)^5. I used the product rule and got to the step where it says y=15x^6(3x-2)^4+6x^5(3x-2)^5. My teacher then wrote after this 3x^5(3x-2)^4(5x+2(3x-2). I am very confused as how he simplified to that can somone please help me
I will assume your derivative answer is correct, but not simplified
Your teacher wants you to simplify it by using a common factor
Notice 3x^5 is a common factor, so is (3x-2)^4, so ....
15x^6(3x-2)^4+6x^5(3x-2)^5
= 3x^5(3x-2)^4 [ 5x + 2(3x-2) ]
= 3x^5 (3x-2)^4 (11x - 4)
your teacher should have simplified it one more step