Question #1f8f7

1 Answer
Nov 26, 2017

1/(1+xln(3))11+xln(3)

Explanation:

We can let u=1+xln(3)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))ddx(log3(1+xln(3)))=ddu(log3(u))ddx(1+xln(3))

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

Since ln(3)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))