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Title: Differentials of higher orders (Mathematics)
Description: Comprehensive notes and practicals (Problems and Solutions) covering: -Differentials of higher orders
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Suppose we have a function of
two variables z=f(x,y)
...


The differential of the second
order is determined by the
formula
2
d z  d(dz )
...


 z
z 
d z  d dx  dy  
y 
 x
2

'

 z
z 
  dx  dy  dx 
y  x
 x
'

 z
z 
  dx  dy  dy 
y  y
 x

 z
z 
  2 dx 
dy dx 
yx 
 x
2
2
 z
z 
 
dx  2 dy dy
...

x
yx
y
2

2

2

2

z 2
z
z 2
d z  2 dx  2
dydx  2 dy
...

y 
 x
2

Similarly, the formula for
calculating the differential of
the n-th order in a symbolic
form is:
n


 
d z   dx  dy   z
...

3

2

Answer:

d z  6xy dx 
2

2

2

 12x ydxdy  2x dy
Title: Differentials of higher orders (Mathematics)
Description: Comprehensive notes and practicals (Problems and Solutions) covering: -Differentials of higher orders
Buy These NotesPreview