Final answer:
To find the value of (dy)/(dx), differentiate the given equation with respect to x and isolate (dy)/(dx).
Step-by-step explanation:
To find the value of (dy)/(dx) at a given point, we need to find the derivative of the given equation with respect to x. Let's differentiate the equation:
x^3y + y^2 - x^2 = 5
Differentiating both sides with respect to x, we get:
3x^2y + x^3(dy/dx) + 2yy' - 2x = 0
Now we can solve for (dy/dx) by isolating it:
x^3(dy/dx) = -3x^2y + 2x - 2yy'
dy/dx = (-3x^2y + 2x - 2yy')/(x^3).