Implicit Differentiation with Two Equations - Maple Programming Help

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Implicit Differentiation with Two Equations

Description

Using implicit differentiation, compute the derivatives dydx and dzdx implicitly from the equations fx,y,z=gx,y,z and Fx,y,z=Gx,y,z. 

 

Implicit Differentiation with Two Equations

Enter equations:

y22 x z=1

y22xz=1

(1)

x2cosx z=y

x2cosxz=y

(2)

Obtain dydx:

implicitdiff,, y,z, y,x

2xsinxzy1

(3)

Obtain dzdx:

implicitdiff,,y,z,z,x

2yx+zsinxzyzsinxzy1x

(4)

Stepwise Calculation:

Replace y with yx and
z with zx:

eval,, y=yx,z=zx

yx22xzx=1,x2cosxzx=yx

(5)

Apply ddx:

diff,x

2yxⅆⅆxyx2zx2xⅆⅆxzx=0,2x+sinxzxzx+xⅆⅆxzx=ⅆⅆxyx

(6)

Solve for both derivatives:

solve, diffyx,x,diffzx,x1

ⅆⅆxyx=2xsinxzxyx1,ⅆⅆxzx=2yxx+zxsinxzxyxzxsinxzxyx1x

(7)

Replace yx and zx with y and z, respectively:

dy__dx__, dz__dx__=evalrhs1,rhs2,yx=y,  zx=z

dydxdzdx=2xsinxzy12yx+zsinxzyzsinxzy1x

(8)

Commands Used

diff, eval, implicitdiff, isolate, rhs

See Also

Student[Calculus1][DiffTutor]


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