Work authorization limits for dependents

I am originally from India but I was working in the US for the last 6 years. I have recently moved to Dusseldorf from the US with my spouse who is currently an EU Blue Card holder. As a dependent, I have also received a German Residence permit valid for 4 years and as far as my understanding goes, I am now authorized to take up a job in Germany. My question is - am I eligible to take up a job only in Germany, or is my work authorization valid throughout the EU - for example, can I join a company in Eindhoven, Netherlands without the need for the employer to file for a separate work authorization for me? I have a Masters degree from Spain if that makes any difference. Thanks for your valuable suggestions in advance.