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**.

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**.

Calculate:

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

S = x²dS = 2x dx

d(S)= 2·2· 0.001 = 0.004 m²

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