Please explain the following: If x + y = xy, then dy/dx = ?

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Given the equation.

x + y= xy

We need to find dy/dx

We will use implicit differentiation.

==> (x+y)' = (xy)'

==> x' + y' = (x)y' + x'(y)

==> 1 + y' = xy' + y

Now we will combine terms with y' on the left side.

==> y'...

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Given the equation.

x + y= xy

We need to find dy/dx

We will use implicit differentiation.

==> (x+y)' = (xy)'

==> x' + y' = (x)y' + x'(y)

==> 1 + y' = xy' + y

Now we will combine terms with y' on the left side.

==> y' - xy' = y-1

==> y'(1-x)= y-1

==> y'= (y-1)/(1-x)

==> dy/dx = (y-1)/(1-x)

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