If x + y = xy, then dy/dx =Please explain step by step.

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

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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jacqueshaw | Student | (Level 1) Honors

Posted on

xy=x+y

x+y-xy=0

dy/dx=1+dy/dx-(yd/dx x+xd/dx y)

= 1+dy/dx-(y+xdy/dx)

= 1+dy/dx-y-xdy/dx

=dy/dx-xdy/dx=y-1

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

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

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