To find the gradient of a tangent to a curve y=f(x) at a given point x=a:

firstly differentiate the equation of the curve in order to find \displaystyle\frac{dy}{dx} ,

secondly substitute into this expression the value x=a.

## Summary/Background

If y = ax^n then \displaystyle\frac{dy}{dx} = anx^{n-1} and if y = a then \displaystyle \frac{dy}{dx} = 0, where a is a constant.

These work for all values of n, positive or negative, decimal or fraction.

These work for all values of n, positive or negative, decimal or fraction.

## Software/Applets used on this page

## Glossary

### differentiate

to find the derivative of a function

### equation

A statement that two mathematical expressions are equal.

### gradient

The slope of a line; the angle of its inclination to the horizontal.

### tangent

1. The trigonometrical function defined as opposite/adjacent in a right-angled triangle.

2. A straight line that touches a curve at one point.

2. A straight line that touches a curve at one point.

### work

Equal to F x s, where F is the force in Newtons and s is the distance travelled and is measured in Joules.