How do I use the product rule for differentiation?

You should use the product rule when you have a function f(x), which you can't differentiate straight away. But which can be written in the form f(x)=g(x)h(x), where g(x) and h(x) are functions that you do know how to differentiate. Then f'(x)= g(x)h'(x)+h(x)g'(x). This may seem very abstract but an example will make it clear how to use this in practice. Say we wanted to differentiate f(x)=xex. At first glance this appears difficult. It is not a 'standard' function which we know how to differentiate. But we see if we set g(x)=x and h(x)=ex, that f is of the required form to apply the product rule. Because we know that g'(x)=1, and h'(x)=ex. So applying the product rule we see f'(x)=(1)(ex)+x(ex). Which we can simplify to ex(1+x).

Answered by Harry V. Maths tutor

2024 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Why does 'x' need to be in radians to differentiate 'sin x'?


The lines y = 3x² - x + 5/2 intersects the line y = x/2 +7 at two points. Give their coordinates. Show your working


Differentiaate the folowing equation with respect to x: y=4x^3-3x^2+9x+2


Find dy/dx when y = 5x^6 + 4x*sin(x^2)


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 2013–2024

Terms & Conditions|Privacy Policy