# Chain Rule & Substitution in Partial Derivatives

• Oct 7th 2010, 02:44 AM
cutiemike1
Chain Rule & Substitution in Partial Derivatives
THIS IS MY EFFORT:
I just wanted to know if there are mistakes in my work...

#1
http://i104.photobucket.com/albums/m...emike1/pd1.jpg

#2
http://i104.photobucket.com/albums/m...emike1/pd2.jpg

THANKS FOR THOSE WHO WILL HELP ^_^
• Oct 7th 2010, 05:26 AM
HallsofIvy
Those are correct. However, I notice that in using chain rule for the second problem, you have
$\frac{\partial u}{\partial t}= 2e^{\frac{y}{x}}sec^2 t$
while using direct substitution, you get
$\frac{\partial u}{\partial t}= 2e^{2tan t}sec^2 t$

Those are, of course, the same because $x= 2r cos t$ and $y= 4r cos t$ so that $\frac{y}{x}= \frac{4r cos t}{2r cos t}= 2 tan t$

but the second, with only the variable t is the better expression.
• Oct 7th 2010, 05:39 AM
cutiemike1
oh yeah!! since it is with respect to t..thanks a lot for that one...

however, i am just wondering in my number 1 answer...try to take a look in Chain Rule the y=re^-s, are the derivatives under it are correct??
• Oct 7th 2010, 05:40 AM
cutiemike1
oh yeah!! since it is with respect to t..thanks a lot for that one...

however, i am just wondering in my number 1 answer...try to take a look in Chain Rule ung y=re^-s, are the derivatives under it are correct??