Question

Find the derivative of function. Do not simplify answer

Answer 1

\[f(x)=9\ln(3x^5+6)\]

Answer 2

We are going to do chain rule.

Answer 3

i tried it and i got 135x^5/3x^5+6

Answer 4

\[
(g\circ u)(x) = 9\ln(3x^5+6)
\]We let \(u(x) = 3x^5+6\) and let \(g(u) = 9\ln(u)\).

Answer 5

What did you get for \(u'(x)\) and \(g'(u)\)?

Answer 6

i did
\[9\frac{ g'(x) }{ g(x) }\]
9x\[\frac{ 15x^4 }{ 3x^5+6 }\]
=\[\frac{ 135x^5 }{ 3x^5+6 }\]

Answer 7

\[9 \frac{ 15x^4 }{ 3x^5+6 }\]

Answer 8

and answer i got 135x^5/3x^5+6

Answer 9

Where did you get the \(x\) in \(9x\) ?

Answer 10

thats times

Answer 11

then why does \(x^4\) become \(x^5\)?

Answer 12

oh thats my mistake

Answer 13

i meant x^4

Answer 14

The fraction can be reduced if you factor.

Answer 15

But since you're not supposed to simplify, I guess you have it correct?