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 )

IA
Answered by Ife A. Maths tutor

3959 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Integrate cos(x)sin^2(x)


Solve x^2 + x=12 by factorising


Integrate by parts the following function: ln(x)/x^3


A triangle has sides A, B and C. The side BC has length 20cm, the angle ABC is 50 deg and angle BAC is 68 deg. a) Show that the length of AC is 16.5cm, correct to three significant figures. b) The midpoint of BC is M, hence find the length of AM


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