14. Find $f_{x}, f_{y}$, and $f_{z}$ for $f(x, y, z)=4 x y+7 x z+y z$.
\[
f_{x}=
\]
\[
f_{y}=
\]
\[
f_{z}=
\]

Step 1 ：The question is asking for the partial derivatives of the function \(f(x, y, z)=4 x y+7 x z+y z\) with respect to \(x\), \(y\), and \(z\).

Step 2 ：Partial derivatives are a type of derivative where we differentiate with respect to one variable while keeping the other variables constant.

Step 3 ：To find \(f_{x}\), we differentiate \(f\) with respect to \(x\) while treating \(y\) and \(z\) as constants.

Step 4 ：To find \(f_{y}\), we differentiate \(f\) with respect to \(y\) while treating \(x\) and \(z\) as constants.

Step 5 ：To find \(f_{z}\), we differentiate \(f\) with respect to \(z\) while treating \(x\) and \(y\) as constants.

Step 6 ：\(f = 4*x*y + 7*x*z + y*z\)

Step 7 ：\(f_x = 4*y + 7*z\)

Step 8 ：\(f_y = 4*x + z\)

Step 9 ：\(f_z = 7*x + y\)

Step 10 ：Final Answer: \(f_{x}=\boxed{4y+7z}\), \(f_{y}=\boxed{4x+z}\), \(f_{z}=\boxed{7x+y}\)