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

3934 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the turning points of the curve (x^3)/3 + x^2 -8x + 5


Solve the differential equation (1 + x^2)dy/dx = x tan(y)


How do you differentiate parametric equations?


Derive 2*x^(3/2)+x+4


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