Tricky Differentiation of Derivative

In summary, The conversation is about deriving a governing equation for conservation of momentum for a non-Newtonian fluid. The equation in question is d/dx(((-dv/dx)^(m-1))*(dv/dx)) where x is the variable, v is a function of x, and m is a constant. The approach involves using the chain rule and product rule to differentiate, resulting in m(dv/dx)^m-1(d^2v/dx^2).
  • #1
olechka722
6
0
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!
 
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  • #2
Hi olechka722! :smile:

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
 

1. What is the difference between derivative and differentiation?

Derivative refers to the rate of change of a function at a specific point, while differentiation is the process of finding the derivative of a function.

2. How do I differentiate a polynomial function?

To differentiate a polynomial function, you can use the power rule which states that the derivative of xn is nxn-1, where n is the power of x.

3. Can I differentiate a constant?

No, the derivative of a constant is always 0 since a constant does not change with respect to any variable.

4. What is the chain rule in differentiation?

The chain rule is a method for finding the derivative of a composite function. It states that the derivative of a composite function f(g(x)) is equal to the derivative of the outer function f evaluated at the inner function g(x), multiplied by the derivative of the inner function g(x).

5. How do I differentiate a logarithmic function?

To differentiate a logarithmic function, you can use the rule d/dx(ln(x)) = 1/x. For a logarithmic function with a base other than e, you can use the change of base formula and then apply the rule.

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