Solving Differentiating a Streamfunction with Maple Help

[neilgregge]

Hello,

I was set the problem to differentiate the following streamfunction in order to find its x and y velocities:

psi=psinought*tanh(y/d)+mu*exp(-((x-L)^2+y^2)/2*sigma^2)*cos(k(y-vt)).

Being the lazy sort I am, I called in Maple.

dpsi/dx worked out perfectly (in that I got the same answer by hand)

dpsi/dy, however, threw up the following:

dpsi/dy=(psinought/d)*(1-tanh(y/d)^2)-(mu*y/sigma^2)*exp(...)*cos(...)-mu*exp(...)*sin(...)*D(k)(y-vt)


the last term D(k)... makes no sense to me. How can differentiating introduce a new variable?

I know I'm probably being a moron, and I'm certainly no expert in using maple, but anyone who can shine a light in my general direction would be muchly appreciated.

 

[George Jones]

*cos(k(y-vt))

Should be k*(y-v*t). Maple has to be told explicitly about multiplication.

Maple applied the chain rule. It interpreted the brackets as saying that k is a function evaluated at argument y-v*t.

 

[neilgregge]

That makes perfect sense. Thank you.