7.1.4

Differentiation

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Derivatives

The derivative of a function, f(x), is the function that describes how the gradient changes as x changes. This is the same as saying that the derivative is the rate of change of an equation.

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Derivatives

  • The derivative of a function can be used to calculate the gradient of the function at any point.
  • The derivative of f(xx) is called f'(xx).
    • f'(xx) can be called "f dash of xx" or "f prime".
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Example

  • A function, f(xx), has the derivative, f'(xx) = 2xx + 5
  • What is the gradient of f(xx) when xx = 3?
    • Gradient at xx = 3 is f'(3).
    • f'(3) = (2 × 3) + 5 = 11
  • f(xx) has a gradient of 11 when xx = 3.

Jump to other topics

1Proof

2Algebra & Functions

2.1Powers & Roots

2.2Quadratic Equations

2.3Inequalities

2.4Polynomials

2.5Graphs

2.6Functions

2.7Transformation of Graphs

2.8Partial Fractions (A2 Only)

3Coordinate Geometry

4Sequences & Series

5Trigonometry

6Exponentials & Logarithms

7Differentiation

8Integration

9Numerical Methods

10Vectors

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