How do you find the derivative of

Braden Hatfield

Braden Hatfield

Answered question

2022-04-15

How do you find the derivative of f(x)=x312x using the limit process?

Answer & Explanation

cm1mmeboulbes21e1

cm1mmeboulbes21e1

Beginner2022-04-16Added 8 answers

Explanation:
f is a polynomial function, so it is (infinitely) differentiable everywhere. Using the alternate definition of the derivative, since we need the general derivative function:
limh0f(x+h)f(x)h=
limh0(x+h)312(x+h)x3+12xh=
limh0x3+3x2h+3xh2+h312x12hx3+12xh=
limh03x2h+3xh2+h312hh=
limh0h(3x2+3xh+h212)h=
limh0(3x2+3xh+h212)=3x2+0+012
=3x212.

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