Question

Struggling with changing parameters.\[T(x,t) = {Q' \over \sqrt {kt} }U(\mu)\] where \[\mu={x\over \sqrt {kt} }\]I need to find Txx. Any help would be a lifesaver!!!

Answer 1

Struggling with changing parameters.\[T(x,t) = {Q' \over \sqrt {kt} }U(\mu)\] where \[\mu={x\over \sqrt {kt} }\]I need to find Txx. Any help would be a lifesaver!!!

Answer 2

and Q' is an arbitrary constant?

Answer 3

I know the answer is \[Txx = {Q' \over (kt)^{3\over2}}U''(\mu)\]. Yep Q is arbitrary

Answer 4

\[
T_x={\partial T\over\partial x}={Q'\over\sqrt{kt}}U'(\mu){\partial\mu\over\partial x}
\]

Answer 5

You are a legend

Answer 6

\[
T_x={Q'\over\sqrt{kt}}U'(\mu){1\over \sqrt{kt}}={Q'\over kt}U'(\mu)
\]

Answer 7

and we differentiate it again

Answer 8

yeah, I get it. Thanks so much

Answer 9

yw. :)