`y = x(6x + 1)^5` Find the derivative of the function.

Expert Answers
sciencesolve eNotes educator| Certified Educator

You need to differentiate the function with respect to x, using the product rule and chain rule, such that:

`y' = x'*(6x + 1)^5 + x*((6x + 1)^5)'`

`y' = 1*(6x + 1)^5 + x*5*(6x + 1)^4*(6x+1)'`

`y' = 1*(6x + 1)^5 +5x*(6x + 1)^4*6`

`y' = (6x + 1)^5 +30x*(6x + 1)^4`

Factoring out `(6x + 1)^4` yields:

`y' = (6x + 1)^4*(6x + 1 + 30x)`

`y' = (6x + 1)^4*(36x + 1)`

Hence, evaluating the derivative of the given function yields `y' = (6x + 1)^4*(36x + 1).`