# Find both first partial derivatives. h(x, y) = e^(-(x2+y2))

Find both first partial derivatives. $h\left(x,y\right)={e}^{-\left(x2+y2\right)}$
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Benedict
Step 1
The given function is $h\left(x,y\right)={e}^{-\left({x}^{2}+{y}^{2}\right)}$.
To find the partial derivatives.
Solution:
The given function is $h\left(x,y\right)={e}^{-\left({x}^{2}+{y}^{2}\right)}$.
Now differentiate partially above function with respect to x,
$\frac{\partial h}{\partial x}={e}^{-\left({x}^{2}+{y}^{2}\right)}×\left(-2x\right)$
$=-2x{e}^{-\left({x}^{2}+{y}^{2}\right)}$
Step 2
Now differentiate partially above function with respect to y,
$\frac{\partial h}{\partial x}={e}^{-\left({x}^{2}+{y}^{2}\right)}×\left(-2y\right)$
$=-2y{e}^{-\left({x}^{2}+{y}^{2}\right)}$