If I was to draw a diagram, like so:

The co-ordinates of P are (x, (

*f*(x)). If the x-coordinate of Q is (x+h) then the y-coordinate of Q is

*f*(x+h). Gradient of PQ = QR/PR

= (

*f*(x+h) -

*f*(x))/h

As Q 'slides down' the curve: In the limit, as Q→P, and h→0, the gradient of the chord PQ approaches the gradient of the tangent at point P.

Gradient of the tangent at P = lim(h→0) (

*f*(x+h)-

*f*(x))/h

This is often referred to as the gradient function written

*f*'(x)

i.e

*f*'(x) = lim(h→0) (

*f*(x+h)-

*f*(x))/h

This limit is used when calculating the derivative of

*f*(x) from first principles. The derivative

*f*'(x) is interpreted as the rate of change of y with respect to x. Hope you understood that