Derivative of a Function.

Let function f be specified in surrounding U of a certain point x0.

f: f(x) = y.

Δy is change in value of function that corresponds to change in value of x-variable Δx.

Thus, we have:

Δy = f(x0 + Δx) - f(x0).

Difference quotient of a function f in a point x0 with a change Δx of a variable x is, then:

Δy = (f(x0 + Δx) - f(x0)) / Δx.

Derivative of a function f in point x0, noted as f'(x0) is difference quotient limit at Δx → 0.

Thus, we have:

Source: [42].

See also, if You wish: Differential of a function.

1 comment:

  1. (EN) derivative of a function f in a point = (PL) różniczka funkcji f w punkcie.