Question

Partial derivatives of e^(x/y)

Answer 1

$$\frac\partial{\partial x}e^{\frac{x}y}=\frac1ye^{\frac{x}y}$$Can you do \(\dfrac\partial{\partial y}\)?

Answer 2

xe^(x/y)?

Answer 3

@oldrin.bataku

Answer 4

Pretend \(x\) is a constant \(k\) and try determining$$\frac{d}{dy}e^{\frac{k}y}$$Note you'll need to use the chain rule... can you figure out the derivative of \(\dfrac{k}y\)?

Answer 5

Isn't the derivative of k/y: -k/(y^2)

Answer 6

Right! So instead of \(k\) we have \(x\) and it's a *partial* derivative:$$\frac\partial{\partial y}\frac{x}y=-\frac{x}{y^2}$$Can you try completing \(\dfrac\partial{\partial y}e^{\frac{x}y}\)?

Answer 7

\[-\frac{ x }{ y ^{2} }*e ^{\frac{ x }{ y }}\]

Answer 8

@oldrin.bataku