Question

Find the derivative by the limit process: f(x)=x^3-12x
Can someone explain it with work, pleasssse?

Answer 1

Okay This is gonna take a minute to type up. but i have all steps for you.

Answer 2

\[\lim_{h \rightarrow 0}[x ^{3}-12x]/h\]
\[\lim_{h \rightarrow 0}[(x+h)^{3}-12(x+h)]/h\]
Expand the terms out and it becomes this ugly thing.
x^3+3xh^2+3hx^2+h^3+12x+12h all over h.
Then break the terms up each one.
x^3/h + 3xh^2/h + 3x/h + h^3/h + 12x/h + 12h/h
When we have a value that is over h, it diverges to 0.
So we now have 0+0+3x^2+0+0+12
Hope this helps.
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