Question

Find the derivative of the function

h(x) = ln(9x+1/4x-2)

Answer 1

\[\huge \log(\frac{ a }{ b })=\log(a)-\log(b)\]
Use this rule of logarithms to split your problem into two separate logs.
\[a=9x+1\]\[b=4x-2\]

Answer 2

ok, then i would just have to subtract a from b to get an answer?

Answer 3

No, we haven't taken a derivative.
Applying the log rule just makes it EASIER to take a derivative.
But you still need to find the derivative of the logs.

Answer 4

i see. so a' = 9 while b' = 4, correct?

Answer 5

Oh when you apply the chain rule? yes i suppose thats true :O don't take the derivative with a's and b's though XD I was just stating a rule for u hehe

Answer 6

\[\large \ln(\frac{ 9x+1 }{ 4x-2 })=\ln(9x+1)-\ln(4x-2)\]
I was just suggesting that you use that rule to write your problem like this.

Answer 7

oh alright

Answer 8

@zepdrix , so my next step would be finding the derivative of both equations?

Answer 9

Both pieces? yes c: Remember how to take the derivative of the natural log, don't forget the chain rule! :D

Answer 10

so the derivative for the fist piece is 9 and second is 4, what would i do with the chain rule

Answer 11

Understand how to do the first piece? :o