When do I use the product rule as opposed to the chain rule?

The product rule is used when two functions of x are multiplied by each other, hence, product. So this can be used to differnetiatate 3x2* x+1 or more complex functions like sinxcosx.

The chain rule is used anytime you see a function inside another function. So in our previous example our two functions were 3x2 and x+1. It would be necessary to use the chain rule if it were 3(x+1)2. This is a function inside a function as the x+1 term has repleced the x term in 3x2. As this is only a sqaured turn, using binomial expansion one could expand the brackets getting 3x2 + 6x + 1 and then differentiate, but using the chain rule is much quicker and avoids misktakes, especally when dealing with bigger indicies.

LU
Answered by Lota U. Maths tutor

3394 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

A curve has equation y = 20x - x^2 - 2x^3 . The curve has a stationary point at the point M where x = −2. Find the x- coordinate of the other stationary point of the curve


Solve ln(2x-3) = 1


Find the derivative of the function y = (2x + 12)/(1-x)


g(x) = ( x / (x+3) ) + ( 3(2x+1) / (x^2 + x - 6) ). Show that this can be simplified to: g(x) = (x+1) / (x-2).


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences