Final answer:
The derivative of a multivariable function can be expressed as the sum of its partial derivatives. Derivative of multivariable function f(x, y) = x^2 + y^3 is 2x + 3y^2, sum of partial derivatives.
Step-by-step explanation:
The derivative of a multivariable function can be expressed as the sum of its partial derivatives. This can be done because the derivative of a sum is equal to the sum of the derivatives.
For example, let's consider a function f(x, y) = x^2 + y^3. The partial derivative with respect to x (denoted as ∂f/∂x) is 2x and the partial derivative with respect to y (denoted as ∂f/∂y) is 3y^2. Therefore, the derivative of f(x, y) is equal to the sum of these partial derivatives, which is 2x + 3y^2.
To find the derivative of a multivariable function, we can express it as the sum of its partial derivatives. For example, consider the function f(x, y) = x^2 + y^3. The partial derivative with respect to x (∂f/∂x) is 2x, and the partial derivative with respect to y (∂f/∂y) is 3y^2.
Therefore, the derivative of f(x, y) is given by the sum of these partial derivatives, which is 2x + 3y^2. This approach simplifies finding the derivative of a multivariable function by breaking it down into its partial derivatives and summing them up.