Log Derivative of a Function: Find Derivatives of f(c,l) with Example"

[beaf123]

Homework Statement

f(c,l) = log(c - ψ(1-l)^θ )

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

Homework Equations

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

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

 

[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.

 

[beaf123]

Thak you. Yes, that is wahrt I did.

 

[Ray Vickson]

Homework Statement

f(c,l) = log(c - ψ(1-l)^θ )

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

Homework Equations

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

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

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.

 

[beaf123]

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

 

[Ray Vickson]

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

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.