- lynda.boyce

I need some calculus help.
the profit (in millions of dollars) derived from selling x units of a certain software is modeled by the following function: P(x) = 0.003x^3 + 100x. If the rate of change in profit, called the marginal profit, is modeled by the derivative of P(x), find P'(x).

- katieb

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- dan815

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- lynda.boyce

can you explain it a little bit?

- dan815

|dw:1434749048222:dw|

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## More answers

- dan815

do you know first principles?

- dan815

where a derivative comes from

- lynda.boyce

I have been thrown into this. I haven't taken algebra since high school and calculus is very new to me

- dan815

i see

- dan815

um start with lines, do you know how to find slope of lines?

- lynda.boyce

I sort of understand derivatives

- dan815

can you summarize a bit of what u know about derivatives

- dan815

id like to know where u stand

- lynda.boyce

ok. if you have y = f(x) then the derivative of f is the function whose value is at the x limit

- dan815

the way I think is best to think about a derivative is rate of change, it is the slope of the tangent line to some function at every point

- lynda.boyce

oh ok
I can see that

- dan815

if you think about it as this, then the first principle definition of a derivative is very natural

- dan815

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- dan815

if you go close and close to the point. the slope of the secant line begins to approach the tangent line at that point

- lynda.boyce

yes

- dan815

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- dan815

from this, we can write the first principle equation, and see why the power rule comes up

- dan815

|dw:1434749924322:dw|

- dan815

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- dan815

soo u want to know why the power rule came about?

- dan815

when
\[f(x) = x^n \]
where n is any random number
then
\[f'(x) = n*x^{n-1}\]

- dan815

you can sub in x^n into first principle to see this formula come about

- lynda.boyce

I think I have it

- dan815

okay :)

- lynda.boyce

thank you

- dan815

well if you are interested in the proof, you can try to work it out, you will have to use the binomial theorem in there

- lynda.boyce

I will try it thanks

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