Differentiation of Profit Functions

[EmmaC]

How do you differentiate the following:

?(x)=15ln(7x)-5(x+15) for all x >0

& why is it concave?


Normally I few problems with differentiation, but the (7x) and (x-15) has left me confused

Regards,
Emma

 

[galactus]

The derivative of ln(7x) is 1/x, via the chain rule. The derivative of a constant is 0, the derivative of 5x is 5.

So, the derivative is:

\(\displaystyle \frac{15}{x}-5\)