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Math Help - differentiation problems

  1. #1
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    differentiation problems

    I am in my first calculus class and I am completely lost. The teacher is very intelligent, but her teaching style is not very effective for me. I have always made great grades in math courses, but I have been doing poorly in this course. My book is Technical Calculus by Peter Kuhfittig and I have a difficult time learning the information from the book. I have a couple of easy problems that I can't figure out how to answer. I was hoping that somebody might be able to answer them and break down the process for me. I have a test on Thursday and I would like to find a free online resource to learn this information. I apologize for asking you to answer questions for me, but I really have no option since I must turn in my homework (graded for correctness) and I don't have a clue how to answer the questions. I will try to help others on this forum when I can.



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  2. #2
    Senior Member mollymcf2009's Avatar
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    Quote Originally Posted by patrickg View Post
    I am in my first calculus class and I am completely lost. The teacher is very intelligent, but her teaching style is not very effective for me. I have always made great grades in math courses, but I have been doing poorly in this course. My book is Technical Calculus by Peter Kuhfittig and I have a difficult time learning the information from the book. I have a couple of easy problems that I can't figure out how to answer. I was hoping that somebody might be able to answer them and break down the process for me. I have a test on Thursday and I would like to find a free online resource to learn this information. I apologize for asking you to answer questions for me, but I really have no option since I must turn in my homework (graded for correctness) and I don't have a clue how to answer the questions. I will try to help others on this forum when I can.




    #32 y = \sqrt{ln(x)} dx

    First, change this to:

    y = (ln(x))^{\frac{1}{2}}

    Then you will need to use the chain rule. Which I assume you have learned?

    Let f(x) = x^{\frac{1}{2}}
    Let g(x) = ln(x)

    So,
    f'( x) = \frac{1}{2}x^{-\frac{1}{2}}
    g'(x) = \frac{1}{x}

    Chain rule = f'(g(x)) \cdot g'(x)

    y' = \frac{\frac{1}{2} (ln(x))^{-\frac{1}{2}}}{x}

    = \frac{1}{2x\sqrt{lnx}}


    #44. r_1 = \frac{r_2}{ln(r_2)}

    You will need to use the quotient rule:

    Let
    f(x) = r_2
    g(x) = ln(r_2)

    f'(x) = 1
    g'(x) = \frac{1}{r_2}

    Quotient rule: \frac{fg' - f'g}{g^2}

    Can you try to solve it?

    #38 y = x^x

    You will need to use the natural log to solve this. Start by taking the natural log of both sides:

    ln(y) = ln(x)^x

    ln(y) = x ln(x)

    Now differentiate with respect to x, using chain rule on the right and product rule on the left:

    \frac{1}{y}y' = x(\frac{1}{x}) + ln(x)

    Then just solve for y'

    #40 y = (sin(x))^x

    This one will use both the chain rule and implicit differentiation like we did in the last one. See if you can try it.
    Good luck!
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  3. #3
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    I am going to start going over it and I will post back after a while. Thank you very much for getting me started down the right track.
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