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Math Help - implicit derivatives

  1. #1
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    implicit derivatives

    Find the slope of the tangent line to the curve
    at the point .

    when i do this i get to 6cos(x)-4sin(y)(dy/dx)+6sinxsiny(dy/dx)-cosy6cosx

    then i get -7/4
    where is my mistake?
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by alexandriaruth View Post
    Find the slope of the tangent line to the curve
    at the point .

    when i do this i get to 6cos(x)-4sin(y)(dy/dx)+6sinxsiny(dy/dx)-cosy6cosx+1=0

    then i get -7/4
    where is my mistake?
    I added something that you missed in red.

    From there, you should have 6\cos(3\pi)-4\sin\left(\tfrac{7}{2}\pi\right)\frac{\,dy}{\,dx}  +6\sin\left(3\pi\right)\sin\left(\tfrac{7}{2}\pi\r  ight)\frac{\,dy}{\,dx}-\cos\left(\tfrac{7}{2}\pi\right)\cos\left(3\pi\rig  ht)=-1 \implies -6-4\frac{\,dy}{\,dx}=-1\implies -4\frac{\,dy}{\,dx}=5\implies \frac{\,dy}{\,dx}=-\frac{5}{4}

    Does this make sense?
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