Derivative as a Function

x

1

function

x

2

x

3

x

sin(x)

cos(x)

x



log(x)

As a pointwise limit, the derivative gives the slope of the tangent to the curve. Varying the point and plotting the tangent slope as a function of

x

yields a new curve, the derivative as a function. It is possible to guess at a formula for the derivative from this curve.