Order the steps of computing f'(x) for f(x) = x² from the limit definition.

Write the difference quotient ((x + h) squared - x squared)/h → Expand the numerator to 2xh + h squared → Cancel one factor of h to leave 2x + h → Let h approach 0 to obtain 2x

Mathematics I / The Derivative

Practice question · Put in order

Order the steps of computing f'(x) for $f(x) = x^{2}$ from the limit definition.

Write the difference quotient ((x + h) squared - x squared)/h
Expand the numerator to 2xh + h squared
Let h approach 0 to obtain 2x
Cancel one factor of h to leave 2x + h

Hints

The cancellation is what makes the limit computable, and it must come before the limit.
You cannot set h to 0 while it still sits in a denominator.

Show the answer

Write the difference quotient ((x + h) squared - x squared)/h
Expand the numerator to 2xh + h squared
Cancel one factor of h to leave 2x + h
Let h approach 0 to obtain 2x

Why

Substituting h = 0 before cancelling gives 0/0 and no information; cancelling first is legal because h is never actually 0 in the limit process. Every derivative from first principles follows this same pattern: expand, cancel the h, then take the limit.

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Order the steps of computing f'(x) for f(x)=x2f(x) = x^{2}f(x)=x2 from the limit definition.

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Order the steps of computing f'(x) for $f(x) = x^{2}$ from the limit definition.