Question Find the gradient of the function $f(x, y) = x e^{xy^2} + \cos y^2$.

Studdy Solution
Substitute the partial derivatives from steps 10 and 23 into the gradient vector.
$$\nabla f(x, y) = \left( e^{x y^2} (x y^2 + 1), 2x^2y e^{x y^2} - 2y \sin(y^2) \right)$$
The gradient of the function $f(x, y) = x e^{x y^2} + \cos(y^2)$ is:
$$\nabla f(x, y) = \left( e^{x y^2} (x y^2 + 1), 2x^2y e^{x y^2} - 2y \sin(y^2) \right)$$