How do you use the definition of a

Aldo Fernandez

Aldo Fernandez

Answered question

2022-04-12

How do you use the definition of a derivative to find the derivative of f(x)=x4?

Answer & Explanation

coesarfaujs3t

coesarfaujs3t

Beginner2022-04-13Added 11 answers

The definition of derivative tells us that for a small increment h we can write:
f(x)=limh0f(x+h)f(x)h
in our case:
f(x)=limh0(x+h)4x4h
=limh0x4+6h2x2+4hx3+4h3x+h4x4h=
=limh0h(6hx2+4x3+4h2x+h3)h=
as h0
=6hx2+4x3+4h2x+h3=4x3

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