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calculus

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Find the equation of the tangent to the curve sin(x+y)=xy at the origin.

  • calculus -

    differentiate implicitly

    cos(x+y) (1 + dy/dx) = x dy/dx + y
    at (0,0_
    cos(0)(1+dy/dx) = 0+0
    1(1+dy/dx) = 0
    dy/dx = -1

    so slope is -1 , and y-intercept is 0

    equation of tangent: y = -x

  • calculus -

    Thank you!!!

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