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Math Help - Need help with implicit differentiation

  1. #1
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    Need help with implicit differentiation

    Hi, I'm having an issue using implicit differentiation. I don't think I'm doing it correctly on the first step.

    Equation: "Find dy/dx by implicit differentiation and evaluate the derivative at the given point"
    tan (x+y) =x , (0,0)

    What I have:
    <br />
sec^2(x+y) (1+y') = (1)
    <br />
sec^2(x+y)+y'sec^2(x+y)<br />
    <br />
y'=\frac {1-sec^2(x+y)}{sec^2(x+y)}

    however, the answer for the first part is -sin^2(x+y). Thanks in advance.
    Last edited by cynlix; October 7th 2009 at 04:54 PM.
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  2. #2
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    Quote Originally Posted by cynlix View Post
    Hi, I'm having an issue using implicit differentiation. I don't think I'm doing it correctly on the first step.

    Equation: "Find dy/dx by implicit differentiation and evaluate the derivative at the given point"
    tan (x+y) =x , (0,0)

    What I have:
    <br />
sec^2(x+y) (1+y') = (1)
    <br />
sec^2(x+y)+y'sec^2(x+y)<br />
    <br />
y'=\frac {1-sec^2(x+y)}{sec^2(x+y)}

    however, the answer for the first part is -sin^2(x+y). Thanks in advance.
    same thing ...

    \frac{1-\sec^2(x+y)}{\sec^2(x+y)}

    multiply numerator and denominator by \cos^2(x+y) ...

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

    -[1 - \cos^2(x+y)]

    -\sin^2(x+y)

    ... review your trig identities.
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