Applications of Derivatives · Applied Problems

Differentials

dy = f'(x)\, dx

The differential dy approximates the change in y for a small change dx. Used for error estimation and approximation.

2 worked examples
15 in Applications of Derivatives

Worked examples

Use differentials to approximate the change in y = x³ when x changes from 2 to 2.01.

dy = f'(x) dx = 3x² dx
dy = 3(4)(0.01) = 0.12

Answer: dy = 0.12 (actual Δy = 0.120601)

1 more worked examplePremium

A square is measured as 10 cm on a side with a possible error of ±0.05 cm. Use differentials to estimate the error in the computed area.

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Common questions

What is the Differentials?

The differential dy approximates the change in y for a small change dx. Used for error estimation and approximation. It is one of the applications of derivatives formulas in the CalcRef reference.

How do you use the Differentials?

Worked example. Use differentials to approximate the change in y = x³ when x changes from 2 to 2.01. dy = f'(x) dx = 3x² dx. dy = 3(4)(0.01) = 0.12. Answer: dy = 0.12 (actual Δy = 0.120601).

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