# Example of implicit differentiation

• December 7th 2010, 08:27 PM
jameskw
Example of implicit differentiation
I cant seem to solve this problem:

the gas law for an ideal gas with fixed mass m and with gas constant R is PV=mRT. show that
$T (\nabla P / \namba T) (\nabla V / \nabla T) =mR$

can anyone solve this with explanations?

here is my attempt:

$(\nabla P / \nabla T)V=mR$
$(\nabla P / \nabla T)=mR/V$

$(\nabla V / \nabla T)P=mR$
$(\nabla V / \nabla T)=mR/P$

$T (\nabla P / \namba T) (\nabla V / \nabla T) =mR$
=
$T (mR/V) (mR/P) =mR$

which i dont think is right..