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Total Differential
- Thread starter JJ007
- Start date
galactus said:Total differential:
\(\displaystyle df=f_{x}(x,y)dx+f_{y}(x,y)dy\)
Take the partial w.r.t x and y.
For x, differentiate x leaving y constant.
For y, differentiate y leaving x constant.
\(\displaystyle \frac{1}{y}dx+x dy\)
\(\displaystyle e^ydx+yxe^ydy\)
For x/y:
\(\displaystyle f_{x}=\frac{1}{y}dx\)
\(\displaystyle f_{y}=\frac{-x}{y^{2}}dy\)
For \(\displaystyle xe^{y}\)
y is a constant: To make it easier, sub in a constant. Say, 1. Then, differentiate. It may help.
\(\displaystyle f_{x}=e^{y}dx\)
x is a constant:
\(\displaystyle f_{y}=xe^{y}dy\)
See how I got those?.
\(\displaystyle f_{x}=\frac{1}{y}dx\)
\(\displaystyle f_{y}=\frac{-x}{y^{2}}dy\)
For \(\displaystyle xe^{y}\)
y is a constant: To make it easier, sub in a constant. Say, 1. Then, differentiate. It may help.
\(\displaystyle f_{x}=e^{y}dx\)
x is a constant:
\(\displaystyle f_{y}=xe^{y}dy\)
See how I got those?.
galactus said:For x/y:
y is a constant: To make it easier, sub in a constant. Say, 1. Then, differentiate. It may help.
\(\displaystyle f_{x}=e^{y}dx\)
x is a constant:
\(\displaystyle f_{y}=xe^{y}dy\)
See how I got those?.
Oops. That y was actually a 1. Thanks.