# Thread: Differential for func of the general form y = (a+b)^(1/z)

1. ## Differential for func of the general form y = (a+b)^(1/z)

Hi,

I was wondering if someone could enlighten me as to how I would find the partial differential for:
$
q = \left(k^{\rho} + l^{\rho} \right)^{\frac{1}{\rho}}
$

trying to find:
$
\frac{\partial q}{\partial l}, \mbox{whilst holding k const}
$

2. You can write...

$\displaystyle q= e^{\frac{\ln (k^{\rho} + l^{\rho})}{\rho}$ (1)

... and then remember that for an $q(l)= e^{\varphi(l)}$ is...

$\displaystyle \frac{d q}{dl} = e^{\varphi(l)}\ \frac{d \varphi (l)}{dl}$ (2)

Kind regards

$\chi$ $\sigma$