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# Little help with math. Integral & Derivative

Klaw 2
I have a math test in a few days and I don't know a few formulas for sure..
I checked them at school they should be correct now.
Formula = f(x)
Derivative = f'(x)
Integral = F(x)
With a being a constant number [like 2].
With g being a constant number [8].
and u is something with x in it [3x] or [5x^2] [(7x+2)^2]
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So if you have the formula f(x) = a*g^u
Then;
f'(x) = a*lng*g^u*u'
and
F(x) = a*(1/lng)*g^u*(1/u') (+c)

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Other formula f(x) = a*sin(u)
f'(x) = u'*a*cos(u)
Correct yes?
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and if you have f(x)= 1/(u) with (u = g*x+a) (no to the power of something).
f'(x) = not req (a*(u^-2))
F(x) = a* ln(u) /u'
metalfreek
In last part its x+ something ie Integration constant. For the other part I really didn't understand what you meant.

Other formula f(x) = a*sin(u)
f'(x) = a*cos(u)
F(x) = a*-cos(u) (+c)
its correct.
Klaw 2
No has help with the one on the top of the list?
Afaceinthematrix
No... not necessarily... basically... think of it like this...

f(x) = 6^(2x+5)
Let u=2x+5
du=2dx
dx=du/2

so basically you'll divide by 2... with those, just use the substitution method (if the professor requires you to show work on the test).

However, change that 2x+5 to another exponent and things get a little more interesting... Dividing by u' will only work if they equation is linear because the derivative will just be a constant. Everything else that you typed up looks correct, I didn't see any mistakes.

Edit:

and if you have f(x)= a* 1/(u) with (u = g*x+b) no to the power of something.
f'(x) = not req (a*(u^-2))
F(x) = ???

I honestly don't understand what you mean here. Are you trying to ask for the integral of f(x)=a/(gx+b)? are a, g, and b constants? If yes, then you just use natural logarithms and you'll have to factor out some constants.
Afaceinthematrix
So how did you do on your math test?
Klaw 2
 Afaceinthematrix wrote: and if you have f(x)= a* 1/(u) with (u = g*x+b) no to the power of something. f'(x) = not req (a*(u^-2)) F(x) = ??? I honestly don't understand what you mean here. Are you trying to ask for the integral of f(x)=a/(gx+b)? are a, g, and b constants? If yes, then you just use natural logarithms and you'll have to factor out some constants.

Kinda late but yeah those are constants but I already know it and corrected it at the top.
As for the test, didnt go so well i screwed up the part with Probabilities but i can do one test again and I'll redo math. Since it was my worst mark by far.
Afaceinthematrix
Klaw 2 wrote:
 Afaceinthematrix wrote: and if you have f(x)= a* 1/(u) with (u = g*x+b) no to the power of something. f'(x) = not req (a*(u^-2)) F(x) = ??? I honestly don't understand what you mean here. Are you trying to ask for the integral of f(x)=a/(gx+b)? are a, g, and b constants? If yes, then you just use natural logarithms and you'll have to factor out some constants.

Kinda late but yeah those are constants but I already know it and corrected it at the top.
As for the test, didnt go so well i screwed up the part with Probabilities but i can do one test again and I'll redo math. Since it was my worst mark by far.

Well you'll do better the second time. The key to calculus is to remember that it's a combination of mostly easy problems with some tricky problems all backed up by a bunch of extremely simple concepts. Once you understand the concepts, you should be able to figure out any problem. Then it simply comes down to practice. Practice hundreds of problems because the more you practice, the more experience you'll have so you'll be able to figure out the problems on the test faster and easier.

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