What is product rule differentiation?

Product rule differentiation, is a form of differentiation which is used to calculate the derivative, i.e. the gradient of the function, of a function f(x) which is made up of one function g(x) multiplied by another function t(x). So given f(x)= g(x).t(x) we can calculate its derivative f'(x). First we calculate the individual derivatives t'(x) and g'(x) we then calculate the derivative of the function f(x) using the formula f'(x)=t'(x)g(x)+g'(x)t(x).For example given the function f(x)=x3sin(x) so t(x)=x3 , t'(x)=3x2 , g(x)=sin(x) g'(x)=cos(x) therefore f'(x)=3x2sin(x)+x3cos(x)

TF
Answered by Thomas F. Maths tutor

4046 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Differentiate 3x^2 + 6x^5 + 2/x


The curve has equation y = x^3 - x^2 - 5x + 7 and the straight line has equation y = x + 7. One point of intersection, B, has coordinates (0, 7). Find the other two points of intersection, A and C.


Split (3x-4)/(x+2)(x-3) into partial fractions


Use the substitution u=cos(2x)to find ∫(cos(2x))^2 (sin(2x))^3dx


We're here to help

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

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences