# Thread: Equality of two expressions involving derivatives.

1. ## Equality of two expressions involving derivatives.

$-u(\rho u)_{\eta} = -[(\rho u^{2})_{\eta} - (\rho u)u_{\eta}]$

When I use the product rule I get the right term but do not know where the left term comes from

2. Originally Posted by davefulton
$-u(\rho u)_{\eta} = -[(\rho u^{2})_{\eta} - (\rho u)u_{\eta}]$
Assuming the subscript denotes differentiation, the left hand side is $-u^2 \rho_\eta - u \rho u_\eta$.
The right hand side can be written as $-( [\rho_nu u^2 + \rho 2 u u_\eta] - u \rho u_\eta)$ which clearly simplifies to the left hand side.