Taylor Series Expansion
2016+Week4
2016+Week4
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Second Partial Derivatives<br />
Following formulas can be verified by taking the limits<br />
To find the<br />
F<br />
xy<br />
partial derivative first use the formula for<br />
h 0 and k 0<br />
F<br />
x<br />
Then apply the approximation for<br />
( f y<br />
)<br />
f xx<br />
( x,<br />
y)<br />
<br />
F(<br />
x<br />
<br />
h,<br />
y)<br />
<br />
2<br />
f<br />
( x,<br />
h<br />
2<br />
y)<br />
<br />
F(<br />
x<br />
<br />
h,<br />
y)<br />
f yy<br />
( x,<br />
y)<br />
<br />
F(<br />
x,<br />
y<br />
<br />
k)<br />
<br />
2<br />
f<br />
( x,<br />
k<br />
2<br />
y)<br />
<br />
F(<br />
x,<br />
y<br />
<br />
k)<br />
F(<br />
x h,<br />
y k)<br />
F(<br />
x h,<br />
y k)<br />
F(<br />
x<br />
f xy<br />
( x,<br />
y)<br />
<br />
4hk<br />
h,<br />
y<br />
<br />
k)<br />
<br />
F(<br />
x<br />
<br />
h,<br />
y<br />
k)
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