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Math Help - [Finite Maths] Derivative Problems

  1. #1
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    [Finite Maths] Derivative Problems

    Hey guys. I'm a newbie here and if this thread is in the wrong place please forgive me. I didn't know where to post derivative questions, so I figured this place would be the most logical.
    I was going through the review questions I had to complete, and off all the 25 examples, Y'm seriously stuck on a few.
    I'm supposed to find the derivatives of the following questions:

    1- f(x) = (e^x + e^-x) / (e^x - e^-x )

    2- g(x) = e^3x-1 . e^x-2 . e^x

    3- f(x) = 1 / x ln x


    Solving any of them is still a big help, and I'd appreciate it if you could show your workings so I could at least understand what you did and why.

    Thanks a lot
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  2. #2
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    Quote Originally Posted by Shamanistic View Post
    Hey guys. I'm a newbie here and if this thread is in the wrong place please forgive me. I didn't know where to post derivative questions, so I figured this place would be the most logical.
    I was going through the review questions I had to complete, and off all the 25 examples, Y'm seriously stuck on a few.
    I'm supposed to find the derivatives of the following questions:

    1- f(x) = (e^x + e^-x) / (e^x - e^-x )

    2- g(x) = e^3x-1 . e^x-2 . e^x

    3- f(x) = 1 / x ln x


    Solving any of them is still a big help, and I'd appreciate it if you could show your workings so I could at least understand what you did and why.

    Thanks a lot
    Do you know the quotient rule?

    It says that if a(x) and b(x) are differentiable functions, the derivative of
    a(x)/b(x) is (a'(x)b(x)-a(x)b'(x))/(b(x)^2) where a'(x) is the derivative of a(x).

    Apply this for number 1 with a(x)=e^x + e^-x and b(x)=e^x - e^-x

    a'(x)=e^x - e^-x
    b'(x)=e^x + e^-x

    so f'(x)= ((e^x - e^-x)^2 -(e^x + e^-x)^2)/((e^x - e^-x)^2)

    for number 2)-is that a product?
    If so use the product rule: if a(x) and b(x) are differentiable functions, the derivative of a(x)b(x)=a'(x)b(x) + a(x)b'(x).

    For number 3) use the quotient rule again with a(x)=1 (remember that a'(x)=0 for constants!) and b(x)=x(ln(x)). An extra hint: you will need the product rule for b'(x).
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  3. #3
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    thanks a lot for your help!

    For your solution for problem 2, I have a question.


    2- g(x) = e^3x-1 . e^x-2 . e^x

    You said I should use the product rule here. What do I do when there are 3 parts in the equation?

    Is it something like this:
    f'(x) = a'(x)b(x)c(x) + a(x)b'(x)c(x) + a(x)b(x)c'(x) ?

    Thanks again
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  4. #4
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    Smile

    i'll take the 3^{rd} question
    we have f(x)=\frac{1}{x \ln x}=\left ( x\ln x \right )^{-1}
    and u should know that \left (f^{r}  \right )'=rf^{r-1}f^{'},
    so \forall x\in (0,\infty) , \left ((x\ln x)^{-1}  \right )'= -1(x\ln x)^{-2} (\ln x+1) =-\frac{1}{\left (x\ln x  \right )^{2}}\times\left (\ln x+1  \right ) =-\frac{(\ln x+1)}{(x\ln x)^2}
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  5. #5
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    Smile

    Quote Originally Posted by Shamanistic View Post
    thanks a lot for your help!

    For your solution for problem 2, I have a question.


    2- g(x) = e^3x-1 . e^x-2 . e^x

    You said I should use the product rule here. What do I do when there are 3 parts in the equation?

    Is it something like this:
    f'(x) = a'(x)b(x)c(x) + a(x)b'(x)c(x) + a(x)b(x)c'(x) ?

    Thanks again
    if u mean g(x)=\exp(3x-1)\exp(x-2)\exp x
    then u have also g(x)=\exp(5x-3)
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  6. #6
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    Seriously I've got to learn to look at these kinda problems the way you guys do. It's so simple

    Thanks a dozen!
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  7. #7
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    Can anybody help me find the derivative of this problem as well?

    K(x) = (x^2 / 1+x)^2

    Should the square be applied inside the brackets, or should I solve it like this:

    K'(x) = 2.(x^2 / 1+x) . (2x/1)

    I'd appreciate your help
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