       Doing the chain rule

• To: mathgroup at smc.vnet.net
• Subject: [mg128725] Doing the chain rule
• From: tsg.moore at gmail.com
• Date: Wed, 21 Nov 2012 19:47:54 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• Delivered-to: l-mathgroup@wolfram.com
• Delivered-to: mathgroup-newout@smc.vnet.net
• Delivered-to: mathgroup-newsend@smc.vnet.net

```Suppose I have a function u(x, y). I have a transformation from (X, Y) to (x, y) via u(x,y) = U(X,Y) and

X = f(x,y)
Y = g(x,y)

Using Mathematica, how do I compute the derivatives u_x, u_y, u_{xx}, u_{yy}, etc. in terms of U?

For example,
u_x = f_x U_X + g_y U_Y

For example, if
X = y - x
Y = y^2 - x^2

then u_x = -U_X + 2x U_Y.

The problem here is that without knowing the inverses of f(x,y) and g(x,y), I don't know how to get Mathematica to work out the chain rules. For example, can you show me how to compute u_{xx} in mathematica using the above example?

```

• Prev by Date: Re: correlation function
• Next by Date: How to calculate the partial derivative?
• Previous by thread: Re: non optimized inner for loops
• Next by thread: How to calculate the partial derivative?