Question

find all the second - order partial derivatives of the funct

\\( \frac { \partial ^ { 2 } f } { \partial x ^ { 2 } } = 10 + 14 y ^ { 2 } \\)

\\( \frac { \partial ^ { 2 } f } { \partial y \partial x } = \\)

Explanation:

Step1: Integrate $\frac{\partial^{2}f}{\partial x^{2}}$ with respect to $x$

$$\frac{\partial f}{\partial x}=\int(10 + 14y^{2})dx=10x+14y^{2}x + C(y)$$

Step2: Differentiate $\frac{\partial f}{\partial x}$ with respect to $y$

$$\frac{\partial^{2}f}{\partial y\partial x}=\frac{\partial}{\partial y}(10x+14y^{2}x + C(y))=28xy$$

Answer:

$28xy$