Join TSR
 
 About Us | FAQs | Sign in
 
HomeForumsArticlesRevision NotesPersonal StatementsUniversity GuidesHealth & RelationshipsPostgraduate StudyCareersFreshers
Join the UK's largest student community  
Advanced
Search

Join The Student Room Today

Be part of the UK's largest and fastest growing student community.

It's free to join and a lot of fun - Get inspired, express your ideas, interact and share

Join The Student Room Today

Revision:Differentiation

From The Student Room

TSR Wiki > Study Help > Subjects and Revision > Revision Notes > Mathematics > Differentiation

Differentiation allows us to find rates of change, for example, it allows us to find the rate of change of gradient on a curve. There are a number of simple rules which can be used to work out the derivative easily.


(diagram missing)


Contents

Notation

There are a number of ways of writing the derivative:

  1. If \displaystyle y = x^2,\ \frac{dy}{dx} = 2x
    This means that if \displaystyle y = x^2, the derivative of \displaystyle y, with respect to \displaystyle x is \displaystyle 2x.
  2. \displaystyle \frac{d (x^2)}{dx} = 2x
    This says that the derivative of \displaystyle x^2 with respect to \displaystyle x is \displaystyle 2x.
  3. If \displaystyle f(x) = x^2,\ f'(x) = 2x
    This says that is \displaystyle f(x) = x^2, the derivative of \displaystyle f(x) is \displaystyle 2x.


Finding the Gradient of a Curve

Example

What is the gradient of the curve \displaystyle y = 2x^3 when

\displaystyle x = 3.


\displaystyle \frac{dy}{dx} = 6x^2


When \displaystyle x = 3,\ \frac{dy}{dx} = 6\times 9 = 54.


Comments

This is a rather basic article - perhaps not enough detail to explain what differentiation is and how to do it. Needs the general rule including for basic polynomials (with positive whole number powers for C1 and fractional and negative powers for C2).

Retrieved from "http://thestudentroom.co.uk/wiki/Revision:Differentiation"
Article Tools:  Create New Article  |  Report This Article  |  This Article's History  |