Tricky Differentiation of Derivative

[olechka722]

I am having trouble remembering the correct approach here. This is in regards to deriving a governing equation for conservation of momentum for a non-Newtonian fluid. I thought about posting in engineering, but it is more of a calculus question:

d/dx(((-dv/dx)^(m-1))*(dv/dx)) where we are differentiating with respect to x, v is a function of x, and m is some value, not necessarily in integer.

I thought about treating dv/dx as f(x) and doing the chain rule and then the product rule, but am unsure. This step is skipped in the derivation I am looking at, and I would love to figure out the math behind it. Thanks!

 

[tiny-tim]

Hi olechka722!

If you mean d/dx{(dv/dx)^m-1(dv/dx)},

that's just d/dx{(dv/dx)^m},

= m(dv/dx)^m-1d²v/dx²