How do you differentiate #y=(6+7x)/(14x+9)#?
This is just a basic quotient rule problem. The general formula for quotient rule is as follows:
Now, all we have to do is plug in everything.
The derivatives you need to take here are quite simple, as both of your functions are linear. In any case, let's take them up:
Now we just plug this back:
Usually, it's best to leave this answer as is, as expanding doesn't get you anywhere. In this case, however, let's expand the numerator:
As you can see, the
And that is your final answer!
If you're struggling with the Product and Quotient rule, I'd recommend watching this video by Professor Leonard. It's a long video, but he really talks about it thoroughly, and it will help you understand the concepts better.
Hope that helped :)