Get the answer to "Find the first partial derivatives. g(x,y)=exy"

facas9

Answered question

2021-05-17

Find the first partial derivatives.

g (x, y) = e^{\frac{x}{y}}

Clelioo

Skilled2021-05-18Added 88 answers

Calculation:
Consider the provided function is,

g (x, y) = e^{\frac{x}{y}}

Partially derivative of the function

g (x, y) = e^{\frac{x}{y}}

with respect to x.

g_{x} (x, y) = \frac{\partial}{\partial x} (e^{\frac{x}{y}})

= e^{\frac{x}{y}} (\frac{1}{y})

= \frac{1}{y} e^{\frac{x}{y}}

Partially derivative of the function

g (x, y) = e^{\frac{x}{y}}

with respect to x.

g_{y} (x, y) = \frac{\partial}{\partial y} (e^{\frac{x}{y}})

= e^{\frac{x}{y}} (\frac{x}{y^{2}})

= \frac{- x}{y^{2}} e^{\frac{x}{y}}

Therefore, the first partial derivatives for the function

g (x, y) = e^{\frac{x}{y}} a r e g_{x} (x, y) = \frac{1}{y} e^{\frac{x}{y}} and g_{y} (x, y) = - \frac{x}{y^{2}} e^{\frac{x}{y}}

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