Partial Derivative of w = xe^(y/z) | Homework Solution

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SUMMARY

The discussion focuses on finding the partial derivatives of the function w = xe^(y/z). The correct partial derivatives are confirmed as ∂f/∂x = e^(y/z), ∂f/∂y = (xe^(y/z))/z, and ∂f/∂z = (-y/z^2)(xe^(y/z)). Participants emphasize the importance of using curly brackets in LaTeX for proper formatting of exponents and fractions, recommending "e^{y/z}" and "e^{\frac{y}{z}}" for clarity.

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Homework Statement


Find the partial derivative of ## w = xe^\frac {y}{z} ##.

Homework Equations


N/A

The Attempt at a Solution


## \frac{∂f}{∂x} = e^y/z ##
## \frac{∂f}{∂y} = \frac{xe^y/z}{z} ##
## \frac{∂f}{∂z} = (-yz^-2)(xe^yz^-1) ##

Are theses correct? Thanks everyone.
 
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Yes, they are- though poorly written. In Latex, to get more than one character in an exponent (or denominator or numerator, etc.) put them in "curly brackets"- { }.

"e^{y/z}" gives e^{y/z}.

Even better would be "e^{\frac{y}{z}}" which gives e^{\frac{y}{z}}
 
thanks
 

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