What is the derivative of #f(x) = (x)/(sqrt(73x))#?
1 Answer
We can rewrite the denominator using a property of exponentials that states
Also, another law of exponentials states that
Now, we can use the product rule, where
Thus, we need to find

#g'(x)=1# 
To find
#h'(x)# , we need chain rule, which states that#(dy)/(dx)=(dy)/(du)(du)/(dx)# . Renaming#u=73x# , we have#h(x)=u^(1/2)# , which we can derivate using power rule:
Now, proceeding to the product rule:
An exponential law states that