# Homework Help: Derivation Problem

1. Sep 3, 2010

### Gekkoo

1. The problem statement, all variables and given/known data

I dont manage to derive a function properly :(

2. Relevant equations

u = x^α * [(m-Ax)/B]^β

3. The attempt at a solution

FOC: x^α*ln(x)*????=0

It is the second factor I have a problem with. Preciate any help!

2. Sep 3, 2010

### CompuChip

Are you sure this is precalculus? Because it is not nearly as simple as you seem to think it should be.
Let me assume that your variable is x and that all other letters represent constants.

Then first of all, there are two functions of x being multiplied, so you will need the product rule:
(xα * [(m-Ax)/B]β)' = (xα)' * [(m-Ax)/B]β + xα * ( [(m-Ax)/B]β )'
Then the derivative of xα is not xα ln(x), but if x is the variable it's simply α xα - 1. For the derivative of the second part, you will need the chain rule (you can write it as yβ and get β yβ - 1 dy/dx).

If, for some strange reason, you want to take the derivative with respect to α, however, you are right: you simply get
x^α ln(x) * [(m-Ax)/B]^β
because the whole second factor is simply constant with respect to α.

3. Sep 3, 2010

### HallsofIvy

The natural logarithm only turns up in derivatives of exponential problems, such as the derivative of $a^x$- that is, with the variable, x, in the exponent.

Problems like this, which is just a power of x, with x in the base, are done by the 'power law', $(x^a)'= ax^{a- 1}$ which is true for a and number, not just integers.

4. Sep 3, 2010

### Staff: Mentor

(thread moved to Calculus & Beyond)