Chain Rule Math Example 4

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Example 4

easy
Find the derivative of f(x)=(5x−2)3f(x) = (5x - 2)^3.

Solution

  1. 1
    Outer: u3u^3, inner: u=5x−2u = 5x - 2, inner derivative: 55.
  2. 2
    Chain rule: 3(5x−2)2⋅5=15(5x−2)23(5x-2)^2 \cdot 5 = 15(5x-2)^2.

Answer

f′(x)=15(5x−2)2f'(x) = 15(5x - 2)^2
Apply the chain rule: bring down the power, reduce by one, multiply by the derivative of the inner function.

About Chain Rule

The derivative of a composite function f(g(x))f(g(x)) equals f′(g(x))⋅g′(x)f'(g(x)) \cdot g'(x): the derivative of the outer function evaluated at the inner, times the derivative of the inner.

Learn more about Chain Rule →

More Chain Rule Examples

Example 1 easy

Find the derivative of [formula].

Example 2 medium

Find the derivative of [formula].

Example 3 hard

Find the derivative of [formula].

Example 5 medium

Find the derivative of [formula].

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