Using the limit definition, how do you differentiate f(x)=1-x^{2}?

Noe Wade

Noe Wade

Answered question

2022-04-22

Using the limit definition, how do you differentiate f(x)=1x2?

Answer & Explanation

Litzy Fuentes

Litzy Fuentes

Beginner2022-04-23Added 22 answers

The limit definition of the derivative of a function f(x) is
df(x)dx=limh0f(x+h)f(x)h
If f(x)=1x2
then (by the limit definition)
df(x)dx
=limh0(1(x+h)2)(1x2)h
=limh01x22xhh21+x2h
=limh02xhh2h
=limh02xh
=-2x

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