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

[Calpalned]

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.

 

[HallsofIvy]

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 $e^{\frac{y}{z}}$

 

[Calpalned]

thanks