Question 9

If $f(x, y)=x e^{x^{2}+y^{2}}$, then $f_{y}=$

Answer

Expert–verified

Hide Steps

Answer

So, the final answer is $\boxed{2yx e^{x^{2}+y^{2}}}$.

Steps

Step 1 ：Given the function $f(x, y)=x e^{x^{2}+y^{2}}$, we want to find the partial derivative of the function with respect to $y$.

Step 2 ：The partial derivative of the function with respect to $y$ is $f_{y} = 2yx e^{x^{2}+y^{2}}$.

Step 3 ：So, the final answer is $\boxed{2yx e^{x^{2}+y^{2}}}$.