Find the derivative of x(x+3)^5
First we use the product rule, so we multiply x by the derivative of (x+3)5. To find the derivative of (x+3)5 we use the chain rule. So we have 5(x+3)4. So the first part of our product rule calculation is 5x(x+3)4. The next part of our product rule calculation is the easy bit, (x+3)5 multiplied by the derivative of x. Using the general power rule, we see the derivative of x is 1. So the second part of our product rule calculation is just (x+3)5.
So our final answer is (x+3)5 + 5x(x+3)4. Which we can factorise to (x+3)4(5x+x+3) = (x+3)4(6x+3).
