Find $f_{x}$ and $f_{y}$
\[
f(x, y)=-6 e^{5 x-4 y}
\]

Step 1 ：The function given is \(f(x, y)=-6 e^{5 x-4 y}\). We are asked to find the partial derivatives of this function with respect to \(x\) and \(y\).

Step 2 ：The partial derivative of a function with respect to a variable is the derivative of the function with respect to that variable, treating all other variables as constants.

Step 3 ：For \(f_{x}\), we differentiate \(f(x, y)\) with respect to \(x\), treating \(y\) as a constant. The derivative of \(e^{ax}\) with respect to \(x\) is \(ae^{ax}\), so \(f_{x} = -30 e^{5 x-4 y}\).

Step 4 ：For \(f_{y}\), we differentiate \(f(x, y)\) with respect to \(y\), treating \(x\) as a constant. The derivative of \(e^{ax}\) with respect to \(x\) is \(ae^{ax}\), so \(f_{y} = 24 e^{5 x-4 y}\).

Step 5 ：Final Answer: The partial derivative of \(f(x, y)=-6 e^{5 x-4 y}\) with respect to \(x\) is \(f_{x} = -30 e^{5 x-4 y}\) and with respect to \(y\) is \(f_{y} = 24 e^{5 x-4 y}\). So, the final answer is \(\boxed{f_{x} = -30 e^{5 x-4 y}, f_{y} = 24 e^{5 x-4 y}}\).