How do you use the limit definition of

Trent Fuller

Trent Fuller

Answered question

2022-04-09

How do you use the limit definition of the derivative to find the derivative of f(x)=5x+1?

Answer & Explanation

Alonso Christian

Alonso Christian

Beginner2022-04-10Added 11 answers

Limit definition of derivative:
f(x)=limh0(f(x+h)f(x)h)
Plugging in our function f(x)=5x+1
f(x)=limh0[(5(x+h)+1)(5x+1)h]
Distributing terms in the numerator:
f(x)=limh0[5x+5h+15x1h]
Cancel out terms in the numerator:
f(x)=limh0[5x+5h+15x1h]
f(x)=limh0[5hh]
f'(x)=5

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