Differentiation
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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.

Notation
There are a number of ways of writing the derivative:
(1) If y = x², dy/dx = 2x
This means that if y = x², the derivative of y, with respect to x is 2x.


(2) d (x²) = 2x
     dx
This says that the derivative of x² with respect to x is 2x.

(3) If f(x) = x², f '(x) = 2x
This says that is f(x) = x², the derivative of f(x) is 2x.

Finding the Gradient of a Curve
Example:
What is the gradient of the curve y = 2x³ when x = 3.
dy/dx = 6x²
When x = 3, dy/dx = 6×9 = 54

© Matthew Pinkey

Other Notes in this Category

1. Chain, Product and Quotient
2. Differential Equations
3. Differentiation
4. Differentiation from 1st Principles
5. Differentiation of Trig Funcns
6. Exponentials & Logarithms
7. Implicit Differentiation
8. Integration
9. Integration by Parts
10. Integration by Substitution
11. Tangents and Normals
12. The Second Derivative
13. Uses of Differentiation
14. Volumes of Revolution

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