WOLFRAM|DEMONSTRATIONS PROJECT

Derivative as a Function

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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.