# Thread: First and Second partial dervitives

1. ## First and Second partial dervitives

Am kinda stuck with this function They gave me;

f(x,t)=ln(x^2(t)-t/x)

am asked for all first and second order partial dervitves to make the function simpller i did this

f(x,t)=ln(x^2(t)(1-1/x^3))

to break up the to ln's

i get now =ln(x^2t)+ln(1-1/x^3)

for my second order fxy=0 and for fyx=0 i need someone to confirm these for me is my alebgra correct is what am doing correctby splitting up to logarathimes thank you for ur help!

2. Hello, zangestu888!

They gave me: .$\displaystyle f(x,t)\:=\:\ln\left(x^2t-\tfrac{t}{x}\right)$

and asked for all first and second order partial dervitves.

To make the function simpller i did this:
. . $\displaystyle f(x,t)\:=\:\ln\bigg[x^2t\left(1-\frac{1}{x^3}\right)\bigg]$ to break up the two ln's

i get now: .$\displaystyle \ln(x^2t)+\ln\left(1-\tfrac{1}{x^3}\right)$

For my second order: .$\displaystyle f_{xy}= f_{yx}=0$ . . . . all this is correct.

I would break it up like this . . .

We have: .$\displaystyle f(x,t) \;=\;\ln\left(\frac{x^3t - t}{x}\right) \;=\;\ln\left(\frac{t(x^3-1)}{x}\right)$

. . Then: .$\displaystyle f(x,t) \;=\;\ln(t) + \ln(x^3-1) - \ln(x)$