calc

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1 + x = sin(xy^2)

find dy/dx by implicit differentiation

0 + 1 = cos(xy^2). (x)(2y)dy/dx + (y^2)(1)

1/((x)(2y)dy/dx) = cos(xy^2) + (y^2)

dy/dx = cos (xy^2) + (y^2)....

Can I just divide out the (x)(2y) and leave the dy/dx?

  • calc -

    you needed brackets like this
    0 + 1 = cos(xy^2)*( (x)(2y)dy/dx + (y^2)(1) )
    since you need to get at the dy/dx and since it is inside the bracket, you must expand

    1 = 2xy(cos(xy^2))dy/dx + y^2(cos(xy^2)
    1 - y^2(cos(xy^2) = 2xy(cos(xy^2))dy/dx
    dy/dx = (1 - y^2(cos(xy^2))/(2xy(cos(xy^2)))

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