Answer:
5
Explanation:
To find the derivative of a function at a given point, we need to use the concept of limits and the definition of a derivative. In this case, we are trying to find dy/dx at the point (-1,2) for the given function y^2-2xy+3x^3=5
Since the function is equal to 5, we can assume that y^2-2xy+3x^3-5 =0, then we can find the partial derivative with respect to x and y.
∂/∂x (y^2-2xy+3x^3-5) = -2y + 9x^2
∂/∂y (y^2-2xy+3x^3-5) = 2y - 2x
Now we can substitute the point (-1,2) into the equation,
dy/dx = -2(2) + 9(-1)^2 = -4 + 9 = 5
Therefore, dy/dx at the point (-1,2) is equal to 5
It's important to note that this result is valid only for this specific point, it does not mean that it's the slope of the function in general.