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Math Help - some mixed problems...

  1. #1
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    some mixed problems...

    Hello, if anybody could help me with these problems I would greatlly appreciated it! If you could give me details to the solutions I would really appreciate it as well...

    get the first, and second derivaties and graph the functions:
    1) sin(e)^x

    2) (2(e)^2x - 7e)/(5(e)^3x - 7(e)^2x + 5)

    3) sec(ln(x))

    4) (1/2)ln((1 + x)/(1 - x))

    thank you again...
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by onmiverse View Post
    get the first, and second derivaties and graph the functions:
    1) sin(e)^x
    You want the first two derivatives of:

    f(x)=\sin(e^x)

    You will need the chain rule for the first derivative:

    \frac{d}{dx}h(g(x))=h'(g(x))g'(x)

    Here g(x)=e^x and h(x)=\sin(x)

    For the second you will need the cain rule again but also the product rule.

    CB
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  3. #3
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    What was written for (1) was sin(e)^x which I would interpret as sin^x(e), a constant to the x power. That can be written as e^{sin^x(e)}= e^{xsin(e)} and its derivative is sin(e)e^{xsin(e)}= sin(e)[sin^x(e)]= sin^{x+1}(e).
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by HallsofIvy View Post
    What was written for (1) was sin(e)^x which I would interpret as sin^x(e), a constant to the x power. That can be written as e^{sin^x(e)}= e^{xsin(e)} and its derivative is sin(e)e^{xsin(e)}= sin(e)[sin^x(e)]= sin^{x+1}(e).
    It is more likely just sloppy typing by the OP for \sin(e^x) given the other questions. No doubt they will tell us eventually.

    CB
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