Derivative Math Example 4

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Example 4

easy
Find the derivative of f(x)=7x4−2x+9f(x) = 7x^4 - 2x + 9.

Solution

  1. 1
    Apply the power rule term by term.
  2. 2
    For 7x47x^4: 28x328x^3. For −2x-2x: −2-2. For 99: 00.
  3. 3
    So f′(x)=28x3−2f'(x) = 28x^3 - 2.

Answer

f′(x)=28x3−2f'(x) = 28x^3 - 2
Apply the power rule to each term independently. Constants vanish under differentiation.

About Derivative

The instantaneous rate of change of a function at a single point, defined as the limit of the slope of secant lines.

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More Derivative Examples

Example 1 easy

Find the derivative of [formula].

Example 2 medium

Find the derivative of [formula] and evaluate [formula].

Example 3 hard

Use the limit definition to find the derivative of [formula].

Example 5 hard

Find the derivative of [formula] and evaluate [formula].

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