How do I use the product rule for derivatives?

Imagine a function f(x)=g(x)*h(x)    [that is, two functions multiplied together]

To find the derivative, f'(x)=g'(x)*h(x) + g(x)*h'(x)    

For example, f(x) = (3x2)*(cos x )        [g(x)=3x2  , h(x)=cosx]

f'(x) = (6x)(cos x ) + (3x2)(-sin x )

        =6xcos(x) - 3x2sin(x)

JW
Answered by James W. Maths tutor

3972 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How do you integrate (sinx)^2?


Given that: y = 3x^2 + 6x^1/3 + (2x^3 - 7)/(3x^1/2), x > 0 Find dy/dx, give each term in its simplest form


Find the differential of f(x)=y where y=3x^2+2x+4. Hence find the coordinates of the minimum point of f(x)


The curve C has equation: (x-y)^2 = 6x +5y -4. Use Implicit differentiation to find dy/dx in terms of x and y. The point B with coordinates (4, 2) lies on C. The normal to C at B meets the x-axis at point A. Find the x-coordinate of A.


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:

© 2026 by IXL Learning