How do I find the derivative of two functions multiplied by each other?

To find the derivative of two functions multiplied by each other we would use the product rule.

The product rule: (fg)'(x) = f '(x).g(x) + f(x).g'(x)

First we need to split our function into the two parts that are multiplied by eachother, and label these f and g. For example, h(x) = sin(x)(2x + 1)

For this we would label f(x) = sin(x) and g(x) = (2x + 1)

Now we need to find the derivatives of these, to use in the above formula:

f '(x) = cos(x)  g'(x) = 2

So then we put these together in the formula above to get our answer as follows:

h'(x) = cos(x)(2x + 1) + 2sin(x)

ES
Answered by Eleanor S. Maths tutor

3909 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Given that Sin(A) = 1/sqrt(3), show that Tan(A) = 1/sqrt(2)


differentiate with respect to x. i). x^(1/2) ln (3x),


There's a school in India where only 60% of students have internet access. What is the probability of choosing eight students randomly, five of whom have internet access? (Info: Each student's internet access (or lack of it) is independent from all others


Do y=3x^2+5x+12 and y=3x-8 intercept with each other? If yes, at which point(s)?


We're here to help

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

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning