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Math Help - Please help with these: differentiation of Ln and trig

  1. #1
    Super Member Quacky's Avatar
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    Please help with these: differentiation of Ln and trig

    Hey, have I done these correctly? I'm not confidant of the rules at all, especially with b:

    a) y=3sin^2(x)+sec(2x)
    \frac{dy}{dx}=6cos^2(x)+2sec(2x)tan(2x)

    b) y=[x+ln(2x)]^3

    With this example, I could solve it easily if not for the ]^3 at the end. How would this affect my answer?
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  2. #2
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    skeeter's Avatar
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    Quote Originally Posted by Quacky View Post
    Hey, have I done these correctly? I'm not confidant of the rules at all, especially with b:

    a) y=3sin^2(x)+sec(2x)
    \frac{dy}{dx}=6cos^2(x)+2sec(2x)tan(2x)

    you're forgetting to use the chain rule for the first term

    b) y=[x+ln(2x)]^3

    use the chain rule here, also.
    ...
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  3. #3
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    Quote Originally Posted by Quacky View Post
    Hey, have I done these correctly? I'm not confidant of the rules at all, especially with b:

    a) y=3sin^2(x)+sec(2x)
    \frac{dy}{dx}=6cos^2(x)+2sec(2x)tan(2x)

    b) y=[x+ln(2x)]^3

    With this example, I could solve it easily if not for the ]^3 at the end. How would this affect my answer?
    y=3sin^2(x)
    let u= sin x
    so

     <br />
y=3u^2<br />
    then \frac {dy}{du}=6u <br />
\frac {du}{dx}=cosx

     <br />
\frac{dy}{dx}=\frac{dy}{du} \frac {du}{dx}=6ucosx=6sinxcosx<br />
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  4. #4
    Super Member Quacky's Avatar
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    Thanks for the answers, I'll try the second question now.
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