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Math Help - Implicit Differentation

  1. #1
    Junior Member
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    Implicit Differentation

    If xsin(x)-y^2=xy-4, the value of dy/dx at the point (0,2) is ?

    I don't know how to get the derivative, but if i got it I could solve it easily
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  2. #2
    MHF Contributor Calculus26's Avatar
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    For implicit differentiation :
    1.When differentiating a function of x do it normally d(sinx)/dx =cos(x)

    2. when differentiating a function of differentiate with respect to y and multiply by dy/dx : d(sin(y)/dx = cos(y) dy/dx

    for your problem:

    xsin(x)-y^2=xy-4

    sin(x) + xcos(x) -2ydy/dx = y + xdy/dx

    Now solve for dy/dx:

    sin(x) +xcos(x) - y = (2y +x) dy/dx

    [sin(x) +xcos(x) - y ]/(2y+x) = dy/dx
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