A log derivative

1. Nov 24, 2015

beaf123

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

f(c,l) = log(c - ψ(1-l)^θ )

What is the derivative of this function wrt. l and c?

2. Relevant equations

I know that the derivative of log (x) = 1/x

3. The attempt at a solution

I got wrt c:

1/ c - ψ(1-l)θ

and wrt l: θψ(1-l)^θ-1 / c - ψ(1-l)^θ

2. Nov 24, 2015

RUber

Remember the chain rule.
$\frac{d}{dt} f(g(t)) =f'(g(t)) * g'(t).$
If log is your f, and the stuff inside is your g, your first part, f'(g) would be $\frac{1}{c-\psi (1-l)^\theta}$. Then you will need to multiply by the derivative of g wrt. whichever variable you are looking at.

edit: This may very well be what you did, but without proper parentheses, I can't tell.

3. Nov 24, 2015

beaf123

Thak you. Yes, that is wahrt I did.

4. Nov 24, 2015

Ray Vickson

Those are wrong: you should not be getting
$$f_c(c,l) = \frac{1}{c} - \psi(1-l) \theta$$
which is exactly what you wrote.

5. Nov 24, 2015

beaf123

Yeah. I messed up the paranthesis. Thanks for telling me what I should not be getting though

6. Nov 24, 2015

Ray Vickson

Well, maybe with proper parentheses, and fixing up $(1-l)^{\theta}$, your result could be correct. It would be a shame to lose marks on an assignment by not using parentheses when it really takes little extra time.