DifferentiationDifferentiation from first principles
Differentiation of algebraic and trigonometric expressions can be used for calculating rates of change, stationary points and their nature, or the gradient and equation of a tangent to a curve.
Differentiation is used in maths for calculating rates of change.
For example in mechanics, the rate of change of displacement (with respect to time) is the velocity. The rate of change of velocity (with respect to time) is the acceleration.
The rate of change of a function \(f(x)\) with respect to \(x\) can be found by finding the derived function \(f\textquotesingle(x)\).
For an equation beginning \(y =\), the rate of change can be found by differentiating \(y\) with respect to \(x\). In its notation form this is written as \(\frac{{dy}}{{dx}}\). This is also known as 'Leibniz Notation'.
