Question #1f8f7

1 Answer
Nov 26, 2017

#1/(1+xln(3))#

Explanation:

We can let #u=1+xln(3)# and use the chain rule:
#d/dx(log_3(1+xln(3)))=d/(du)(log_3(u))d/dx(1+xln(3))#

Because of the rule #d/dx(log_a(x))=1/(xln(a))#, we know:
#=1/(u\ln(3))*d/dx(1+xln(3))#

Since #ln(3)# is just a constant, we can solve the other derivative too:
#=1/(ucancelln(3))*cancelln(3)=1/u#

If we resubstitute, we get our final answer:
#1/u=1/(1+xln(3))#