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).

Answered by John Y. Maths tutor

2787 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How to find the derivative of arctan(x)


You are given that n is a positive integer. By expressing (x^2n)-1 as a product of factors, prove that (2^2n)-1 is divisible by 3.


Show that sqrt(27) + sqrt(192) = a*sqrt(b), where a and b are prime numbers to be determined


Find the stationary point of the curve y=3x^2-2x+2 and state the nature of this stationary point.


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences