implicit differentiation (dy/dx) of sq. rt (x+y) = 1 + x^2y^2

Question

anonymous · Answer

so
left hand side derivative with respect to x:
d (sqrt(x+y))/dx = 0.5 * (x+y)^(-0.5) * (1+dy/dx)

right hand side derivative with respect to x:
d(1+x^2y^2)/dx = 2xy^2 + 2y*(dy/dx)*x^2

agree ?

goformit100 · Answer

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anonymous · Answer

implicit means that you supose that actualy y is a function of x, y(x), without actually nowing the actual expretion for it. Then differentiate the $\sqrt {x+y} = 1 + x^2y^2$ keeping this in mind.