Question

Question #1f8f7

Answer 1

`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))`