What is the product rule in differentiation?

The product rule is a special rule that exists for differentiating products of two (or more) functions. It states: If y=uv, then dy/dx= u(dv/dx) + v(du/dx). So when we have a product to differentiate we can use this formula.For example, suppose we want to differentiate y=x2(cos3x). In this question u=x2 and our v=cos(3x). So following the formula, our first step is to differentiate the u and v terms. du/dx=2x and dv/dx= -3sin(3x). We now put all these results into the given formula:dy/dx= u(dv/dx) + v(du/dx) = x2 x (-3sin3x) + 2x x cos3x We can tidy this answer up by noticing there is a common factor of x giving us this as a final answer: dy/dx= x(-3xsin3x+ 2cos3x )

Answered by Ife A. Maths tutor

3878 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

What is differentiation and why is it useful?


Integrate 3x^2 + 4/3 x^5 with respect to x


Why is (x^3 - 7x^2 +13x - 6) divisible with (x-2)?


If f(x)= ( ((x^2) +4)(x-3))/2x find f'(x)


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