For a curve y = f(x) there is an associated function called the derivative or gradient function
The derivative of f(x) is written as f'(x) or
The derivative is a formula that can be used to find the gradient of y = f(x) at any point, by substituting the x coordinate of the point into the formula
The process of finding the derivative of a function is called differentiation
We differentiate a function to find its derivative
What is differentiation from first principles?
Differentiation from first principles uses the definition of the derivative of a function f(x)
The definition is
How do I differentiate from first principles?
Exam Tip
Most of the time you will not use first principles to find the derivative of a function (there are much quicker ways!). However, you can be asked on the exam to demonstrate differentiation from first principles.
Make sure you can use first principles differentiation to find the derivatives of kx, kx2 and kx3 (where k is a constant).