Differentials

If f(x) is a differentiable function, the differential of the function corresponding to the increase of the independent variable, h, is the product f'(x) · h. It is denoted by dy.

Differential

Differential

Differential of a Function

Function Differential

Differential of a Function

The differential at a point represents the increase of the y-coordinate of the tangent, which corresponds to an increase in the independent variable, h.

Examples

Calculate:

Function

Differential of a Function

Function

Differential of a Function

Calculate the increase in the area of a square of 2 m2 when each side is increased by 1mm.

S = x2 dS = 2x dx

d(S)= 2·2· 0.001 = 0.004 m2