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12.2.3 Implicit differentiation

The implicitdiff command can differentiate implicitly defined functions or expressions containing implicitly defined functions. It has three different calling sequences.

Examples

implicitdiff(x^2*y+y^2=1,y,x)
     
2 xy
x2+2 y
          
implicitdiff([x^2+y=z,x+y*z=1],[y(x),z(x)],y,x)
     
−2 xy−1
y+z
          
implicitdiff(x*y,-2x^3+15x^2*y+11y^3-24y=0,y(x),x)
     
2 x3−5 x2y+11 y3−8 y
5 x2+11 y2−8
          
f:=x*y*z:; g:=-2x^3+15x^2*y+11y^3-24y=0:; implicitdiff(f,g,[x,z,y],order=1)
     



2 x3z−5 x2yz+11 y3z−8 yz
5 x2+11 y2−8
,xy


          
implicitdiff(f,g,[x,z,y],order=2,[1,-1,0])
     








    
64
9
2
3
    −
2
3
0








          

In the following example, the value of ∂4 f/∂ x4 is computed at the point (x=0,y=0,z).

pd:=implicitdiff(f,g,[x,z,y],order=4,[0,z,0]):; pd[4,0]
     
−2 z           

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