Unit 4 - Objective 5 - Differentials




The differentials are the change in the variables along the tangent line.

For y = f (x)

  1. dx = x = Differential of independent variable

  2. dx = f ' (x) dx = Differential of dependent variable


Problem 1: Foy y = 3x² - 7x + 2 find dy
y = f (x), so dy = f' dx = (6x - 7) dx

Problem 2:

Problem 3:

Problem 4:




Differentials are used to approximate the change in the dependent variable.

If y = f(x), and the change in x, x, is "small", then the actual change in y = y is approximately equal to dy, the differential.


Use the differential to approximate the change in A = r² when r = 2 cm and r = 0.5 cm

Solution: Here A is function of r, A = f (r) so dA = f' (r) dr = f '(r) r

A dA = 2 r r Now substitute in the values
2(2)(0.5) = 2 cm² 6.28 cm²l


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