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Math Help - Derivatives and tangent line

  1. #1
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    Derivatives and tangent line

    1. Find the derivative of cos(sin(x^2))

    2. Find the derivative of (4 tan(x))/x

    3. Find the equation of the tangent line to the curve y=3 tan(x) at the point ((pi/4) , 3)
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  2. #2
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    gotta redeem myself from my mistake earlier

    ok *cracks fingers*


    open the thumbnail in a new window

    so yah refresh me, tangent line is the first derivative to find the slope then plugged into point-slope form?
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  3. #3
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    Reply

    1
    Last edited by Shyam; October 19th 2008 at 09:57 PM.
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  4. #4
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    Quote Originally Posted by ryukolink View Post
    gotta redeem myself from my mistake earlier

    ok *cracks fingers*


    open the thumbnail in a new window

    so yah refresh me, tangent line is the first derivative to find the slope then plugged into point-slope form?
    Yeah I think so.

    The first one worked great, thanks. With the second one though, I can't tell if it was 4sec^2x(x)^-1 or 4sec^2(x)^-1 Which is it?
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  5. #5
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    argh! I'm sorry I forgot to put another (x) after sec^2, damn my fast typing.. the correct one is <br />
4sec^2x(x)^-1<br />
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  6. #6
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    Quote Originally Posted by ryukolink View Post
    argh! I'm sorry I forgot to put another (x) after sec^2, damn my fast typing
    Oh ok that makes sense. It works now, thanks!
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  7. #7
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    ey calculus is a hard mother, no problem man
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  8. #8
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    Quote Originally Posted by Shyam View Post
    3. equation of curve, y = 3 \tan x

    slope of tangent, \frac{dy}{dx}=3 \sec^2 x

    \left[\frac{dy}{dx}\right]_{(x=\frac{\pi}{4})}=3 \sec^2 \left(\frac{\pi}{4} \right)

    slope=\left[{\frac{dy}{dx}}\right]_{(x=\frac{\pi}{4})}= 6

    equation of tangent at \left( \frac{\pi}{4}, 3 \right) is

    x-\frac{\pi}{4}=6(y-3)

    x-6y+18-\frac{\pi}{4}=0

    x-6y+\frac{72-\pi}{4}=0
    It's saying that the tangent line one isn't right.... (and sorry to be a hassle, but could you put in in slope-intercept form?)
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  9. #9
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    Quote Originally Posted by john11235 View Post
    It's saying that the tangent line one isn't right.... (and sorry to be a hassle, but could you put in in slope-intercept form?)
    You try to put this equation in slpoe-intercept form. You please do not depend completely on others. You solve it , it is easy. And then show your work.
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  10. #10
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    Never mind I got it. Thanks guys!
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