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Math Help - derivative trigonometry

  1. #1
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    derivative trigonometry

    <br /> <br />
f(x) = tanxsinx<br /> <br />

    <br /> <br />
f '(x) = (sec^2x)(sinx) + (tanx)(cosx)<br /> <br />

    this correcT?
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  2. #2
    Super Member 11rdc11's Avatar
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    Yep

    <br />
f '(x) = (sec^2x)(sinx) + (tanx)(cosx)<br />

    You could simplify it a little more

    tan(x)(secx+cosx)
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  3. #3
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    Quote Originally Posted by 11rdc11 View Post
    Yep
    can we simplify this ?
    if so how would u do it?
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  4. #4
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by jvignacio View Post
    <br /> <br />
f(x) = tanxsinx<br /> <br />

    <br /> <br />
f '(x) = (sec^2x)(sinx) + (tanx)(cosx)<br /> <br />

    this correcT?
    Yes, but it can be simplified further:

    Note that \sec^2x\sin x=\frac{1}{\cos^2x}\sin x=\tan x \sec  x and \tan x\cos x=\frac{\sin x}{\cos x}\cos x=\sin x

    So we now see that f '(x) = (\sec^2x)(\sin x) + (\tan x)(\cos x)=\sec x\tan x+\sin x

    --Chris
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  5. #5
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    Quote Originally Posted by Chris L T521 View Post
    Yes, but it can be simplified further:

    Note that \sec^2x\sin x=\frac{1}{\cos^2x}\sin x=\tan x \sec x and \tan x\cos x=\frac{\sin x}{\cos x}\cos x=\sin x

    So we now see that f '(x) = (\sec^2x)(\sin x) + (\tan x)(\cos x)=\sec x\tan x+\sin x

    --Chris
    what if the possible answers were:

    <br />
sinx -<br />
sinxsec^2x -<br />
sinx(sec^2x+1) -<br />
secx - <br />
none of these<br />

    what would you go for?
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  6. #6
    Super Member 11rdc11's Avatar
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    I did this kind of fast but I'm pretty sure it the 3rd option

    <br />
f '(x) =\sec x\tan x+\sin x<br />

    \frac{sinx}{cos^2x} + sinx

    \frac{sinx+sinxcos^2x}{cos^2x}

    \frac{sinx(1+cos^2x)}{cos^2x}

    (sinx)(sec^2x + 1)
    Last edited by 11rdc11; September 11th 2008 at 10:33 PM.
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  7. #7
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    Quote Originally Posted by 11rdc11 View Post
    I did this kind of fast but I'm pretty sure it the 3rd option
    yeah thats what i put but i wasnt sure why we got rid of the tanx and cosx
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