# Find all first partial derivatives. f(x, y) = y^3e^(y/x)

Find all first partial derivatives. $f\left(x,y\right)={y}^{3}{e}^{\frac{y}{x}}$
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Step 1
solution:-
A function $f\left(x,y\right)={y}^{3}{e}^{\frac{y}{x}}$ is given.
The objective is to determine both first partial derivatives.
Step 2
The function z=f(x,y) has two input variables, ‘x’ and ‘y’. It can be differentiated partially with respect to ‘x’ or ‘y’.
When differentiating partially with respect to ‘x’, consider variable ‘y’ as a constant.
The partial derivative obtained after differentiating it with respect to ‘x