How do you find the derivative of

Max Williams

Max Williams

Answered question

2022-04-15

How do you find the derivative of f(x)=x using the formal definition?

Answer & Explanation

Naima Silva

Naima Silva

Beginner2022-04-16Added 9 answers

From the definition of derivative:
limh0(x+hxh)=
I would try to rationalize the numerator (although it seems strange...).
=limh0(x+hxh)(x+h+x)(x+h+x)=
=limh0x+hxh(x+h+x)=
=limh0hh(x+h+x)=
=limh01(x+h+x)= as h0
=12x
fallendreamsit2p

fallendreamsit2p

Beginner2022-04-17Added 14 answers

f(a)=limh0(f(a+h)f(a)h)
=limh0(a+hah)
=limh0((a+ha)(a+h+a)h(a+h+a))
=limh0((a+h)-ah(a+h+a))
=limh0(1a+h+a)
=12a
That is:
f(x)=12x

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