How do you find the derivative using limits

Emilia Hoffman

Emilia Hoffman

Answered question

2022-04-15

How do you find the derivative using limits of f(x)=912x?

Answer & Explanation

Dallelopeelvep2yc

Dallelopeelvep2yc

Beginner2022-04-16Added 15 answers

We will use the limit definition, f(x)=limx0f(x+h)f(x)h.
f(x)=limx0912(x+h)(912x)h
f(x)=limx0912x12h9+12xh
f(x)=limx012hh
f(x)=limx012
f(x)=12
seskew192atp

seskew192atp

Beginner2022-04-17Added 12 answers

This is the formula for finding the derivative using limits:
ddxf(x)=limh0f(xh)f(x)h
Plug in (x-h) wherever you see an x in your f(x) for the first part of your numerator and then just the function itself for the second part of the numerator.
Then, its just basic arithmetic after that:
=limh0(9xh2)(9x2)h
=limh0(182xh2)(9x2)h
=limh0(18x+h2)(18x2)h
=limh018x+h218+x2h
=limh012
=12

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