Equivalence of Derivations in the Wave Equation from Maxwell's Equations

[Valeria]

Homework Statement

I am actually following the derivation of the wave equation from Maxwell equations. And I do not understand one step, because in the task for the derivation I get a slightly different result (maybe they are equivalent, but I am not sure).

Homework Equations

In the attached file:
(1) - starting equation; (2) and (3) - necessary identities; (4) - final result from the book; (5) - my final result.

The Attempt at a Solution

(5) is the equation I got. As you can see, only one term is different. Is equation (5) equivalent then to equation (4)? If yes, how to get from (5) to (4)? If no, what could be incorrect?

 

[Orodruin]

(4) and (5) are equivalent. Use the chain rule.