How do you use the definition of a

Keenan Rhodes

Keenan Rhodes

Answered question

2022-04-10

How do you use the definition of a derivative to show that if f(x)=1x then f(x)=1x2?

Answer & Explanation

Gonarsu2dw8

Gonarsu2dw8

Beginner2022-04-11Added 19 answers

By definition:
f(x)=limh0f(x+h)f(x)h
so, with f(x)=1x we have:
f(x)=limh0(1x+h1x)h
=limh0x(xh)x(x+h)h
=limh0xxhx(x+h)h
=limh0hx(x+h)h
=limh01x(x+h)
=limh01x2+xh
=1x2

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