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12. Partial derivative example ( Enter your problem )
  1. Example `x^3+x^2y^3-2y^2`, derivative order = `x`
  2. Example `x^3+x^2y^3-2y^2`, derivative order = `y`
  3. Example `x^3+x^2y^3-2y^2`, derivative order = `x^2,y`

1. Example `x^3+x^2y^3-2y^2`, derivative order = `x`





`f(x,y)=x^3+x^2y^3-2y^2`
Find Partial derivative, Derivative order = `x`


Solution:
Now,
`del/(delx)(x^3+x^2y^3-2y^2)`

`=del/(delx)(x^3)+del/(delx)(x^2y^3)-del/(delx)(2y^2)`

`del/(delx)(x^2y^3)=2xy^3+0`
`del/(delx)(x^2y^3)`

`=(del/(delx)(x^2))y^3+x^2(del/(delx)(y^3))`

`del/(delx)(y^3)=0`
`del/(delx)(y^3)`

`=3y^2*del/(delx)(y)`

`=3y^2*0`

`=0`


`=(2x)y^3+x^2*0`

`=2xy^3+0`


`del/(delx)(2y^2)=0`
`del/(delx)(2y^2)`

`=4y*del/(delx)(y)`

`=4y*0`

`=0`


`=3x^2+(2xy^3+0)-0`

`=3x^2+2xy^3+0-0`

`=3x^2+2xy^3`

`:.(del)/(del x)(x^3+x^2y^3-2y^2)=3x^2+2xy^3`




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