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Transcript
Objectives
2
At the end of the lesson, you should be able to do the following:
Compute the derivative of multivariable functions.
Compute the total derivative of a given multivariable function.
Total Differentiation
3
Total derivative is defined as:
dnn
udy
y
udx
x
udu
...
This swirly-d symbol, ∂, often called "del", is used
to distinguish partial derivatives from ordinary
single-variable derivatives)...,( nyxfu :Given
Total Differentiation
4
dyy
udx
x
udu
This swirly-d symbol, ∂, often called "del", is used
to distinguish partial derivatives from ordinary
single-variable derivatives
23 yxu :Given
223 yxx
u
yxy
u 32
dyyxdxyxdu 2 3 322
Assessment
5
yxyyxf sintan),( :Given
xyx
f 2sec
yxy
fcostan
Find the total derivative of the given function.
dyyxdxxydu costan sec2
dyy
udx
x
udu