Differentiation

Maths: Edexcel A Level Pure Maths, topic 7.1.4

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.

Derivatives

Derivatives

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

Example

Example

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

Test yourself on Differentiation

The derivative of a function, f(x), is f'(x) = 5x + 10. What is the gradient of f(x) when x = −1?
The derivative of a function, f(x), is f'(x) = $\large\frac{1}{2}$ x² − 3x + 2. What is the gradient of f(x) when x = 4?
The derivative of a function, f(x), is f'(x) = 2x − 1. What is the gradient of f(x) when x = 2?
The derivative of a function, f(x), is f'(x) = 9x³ − 10x. What is the gradient of f(x) when x = −1?

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