Differentiating Powers of x

The gradient of an equation is often written as

This is called the derivative or differential of the equation. The process is known as differentiating.

It gives another equation which can be used to find the gradient of a curve at a point.

The rule for differentiating equations is

If y = kxⁿ

Then

dy dx

= knxn-1

Note: Another way of putting it is... If f(x) = xⁿ, Then f¹(x) = knxⁿ-1