# Use the limit definition of partial derivatives to evaluate f_x(x, y) and f_y(x, y) for the following functions. f(x,y)=x/y

Use the limit definition of partial derivatives to evaluate ${f}_{x}\left(x,y\right)\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}{f}_{y}\left(x,y\right)$ for the following functions.
$f\left(x,y\right)=\frac{x}{y}$
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Step 1
Given function is $f\left(x,y\right)=\frac{x}{y}$
Step 2
Partial derivatives:
${f}_{x}\left(x,y\right)=\frac{\partial f\left(x,y\right)}{\partial x}$
$=\underset{h\to 0}{lim}\frac{f\left(x+h,y\right)-f\left(x,y\right)}{h}$
$=\underset{h\to 0}{lim}\frac{\frac{x+h}{y}-\frac{x}{y}}{h}$
using LHospital
Jeffrey Jordon