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

2789 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Using implicit differentiation, write the expression "3y^2 = 4x^3 + x" in terms of "dy/dx"


Find the co ordinates and nature of the turning points of the curve C withe equation, y=2x^3-5x^2-4x+2


if f is defined on with f(x)=x^2-2x-24(x)^0.5 for x>=0 a) find 1st derivative of f, b) find second derivative of f, c) Verify that function f has a stationary point when x = 4 (c) Determine the type stationary point.


Calculate the integral of (3x+3)/(2x^2+3x) between the limits 39 and 3


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