Question

Find d y / d x by implicit differentiation. x y+x+y-x² y²=0

A) F(x) ={2 x y²+y+1}{-2 x² y-x-1}
B) F(x) = {2 x y² -y}{2 x² y+x}

Answer 1

To find dy/dx for the given equation, apply implicit differentiation term by term, using the product rule for xy and x²y², and then solve for dy/dx.

Step-by-step explanation:

To find dy/dx by implicit differentiation for the equation xy + x + y - x²y² = 0, we need to differentiate both sides of the equation with respect to x. This involves applying the product rule to terms involving the product of x and y and remembering that y is a function of x, which requires the use of the chain rule.

Let's differentiate term by term:

• xy becomes y + x(dy/dx) (product rule)
• x simply becomes 1
• y becomes dy/dx
• -x²y² expands into -2xy² - 2x²y(dy/dx) (product rule)

Combining all these and setting the derivative equal to zero, we then solve for dy/dx, which will give us one of the potential solution forms for F(x).