How/when should I use the product rule for differentiation?

The product rule can be used to differentiate a function that is formed of the product of two other functions;

e.g f(x)=x2ex

the product rule is as follows; if f(x) is split up into u.v (in this case u would be x2 and v would be ex), the derivative of th whole function is (u.dv/dx) + (v.du/dx)

so in this case u=x2, following standard differentiation du/dx= 2x

v=ex, dv/dx=ex

u.dv/dx=x2ex

v.du/dx=2xex

so the whole function differentiated = ex(x2+2x)

 

AT
Answered by Abi T. Maths tutor

6242 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

The curve A (y = x3 – x2 + x -1) is perpendicular to the straight-line B at the point P (5, 2). If A and B intersect at P, what is the equation of B? Also, find any stationary points of the curve A.


Express (3x^2 - 3x - 2)/(x-1)(x-2) in partial fractions


Integrate the expression cos^2(x).


At each point P of a curve for which x > 0 the tangent cuts the y-axis at T, and N is the foot of the perpendicular from P to the y-axis. If T is always 1 unit below N and the curve passes through the point (1,0), find the Cartesian equation of the curve.


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