Question

How do you find derivative of a function with two variables.

Answer 1

To find the derivative of a function with two variables, take the partial derivative of the function with respect to each variable. Treat one variable as a constant and differentiate the function with respect to the other variable.

Step-by-step explanation:

To find the derivative of a function with two variables, we take the partial derivative of the function with respect to each variable. This means that we treat one variable as a constant and differentiate the function with respect to the other variable. Here is a step-by-step example:

Let's say the function is f(x, y) = x^2 + 3xy + y^2. To find the partial derivative with respect to x, we treat y as a constant and differentiate x^2, 3xy, and y^2, separately. The derivative of x^2 with respect to x is 2x, the derivative of 3xy with respect to x is 3y, and the derivative of y^2 with respect to x is 0 since y^2 does not contain x. Therefore, the partial derivative of f with respect to x is 2x + 3y.

We can similarly find the partial derivative with respect to y, by treating x as a constant and differentiating the terms with respect to y. In this case, the derivative of x^2 with respect to y is 0, the derivative of 3xy with respect to y is 3x, and the derivative of y^2 with respect to y is 2y. Thus, the partial derivative of f with respect to y is 3x + 2y.

Answer 2

A function z=f(x,y) has two partial derivatives and y. These derivatives correspond to each of the independent variables and can be interpreted as instantaneous rates of change (that is, as slopes of a tangent line). Similarly, ∂z/∂y represents the slope of the tangent line parallel to the y-axis.