## lynda.boyce one year ago 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).

1. dan815

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2. lynda.boyce

can you explain it a little bit?

3. dan815

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4. dan815

do you know first principles?

5. dan815

where a derivative comes from

6. lynda.boyce

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

7. dan815

i see

8. dan815

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

9. lynda.boyce

I sort of understand derivatives

10. dan815

can you summarize a bit of what u know about derivatives

11. dan815

id like to know where u stand

12. lynda.boyce

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

13. 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

14. lynda.boyce

oh ok I can see that

15. dan815

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

16. dan815

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17. 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

18. lynda.boyce

yes

19. dan815

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20. dan815

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

21. dan815

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22. dan815

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23. dan815

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

24. dan815

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

25. dan815

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

26. lynda.boyce

I think I have it

27. dan815

okay :)

28. lynda.boyce

thank you

29. 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

30. lynda.boyce

I will try it thanks

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