`f(x) = 5x - 4` Find the derivative of the function by the limit process.

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Chapter 2, Review - Problem 2 - Calculus of a Single Variable (10th Edition, Ron Larson).
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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to find derivative using limit definition, such that:

`f'(x)= lim_(Delta x -> 0) (f(x + Delta x) - f(x))/(Delta x)`

`f'(x) = lim_(Delta x -> 0) (5(x + Delta x) - 4 - 5x + 4)/(Delta x)`

`f'(x) = lim_(Delta x -> 0) (5x + 5Delta x -4 + 4 - 5x)/(Delta x)`

Reducing like terms yields:

`f'(x) = lim_(Delta x -> 0) ( 5Delta x)/(Delta x)`

Simplify by `Delta x:`

`f'(x) = lim_(Delta x -> 0) 5`

`f'(x) = 5`

Hence, evaluating the limit of function using limit definition, yields f'(x) = 5.

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