I am trying to find the second derivative of the function(adsbygoogle = window.adsbygoogle || []).push({});

[tex] C:[0,1]^{2} \rightarrow [0,1] ,\quad \mbox{defined by }C=C(u,v) [/tex]

evaluated at

[tex]u=F(x)=1-\exp(-\lambda_{1} x),\quad \lambda_{1} \geq 0 [/tex]

and

[tex]v=G(x)=1-\exp(-\lambda_{2} x),\quad \lambda_{2} \geq 0[/tex]

First I work out the first derivative which is

[tex]\dfrac{dC}{dx} = \dfrac{\partial C}{\partial u}\dfrac{du}{dx}+\dfrac{\partial C}{\partial v}\dfrac{dv}{dx}[/tex]

Now, I have trouble working out the second derivative because it looks like I have to used the chain rule again and there is product rule which involves differentiating

[tex]\dfrac{du}{dx}[/tex]

with respect to u(and v)??

I would appreciate any reply. Thank you guys.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Multivariable chain rule question

**Physics Forums | Science Articles, Homework Help, Discussion**