Question

find the derivative of 6ln(x)+8ln(x+3)-6ln((x^2)+7)

Answer 1

( lnx)' = ...?
( lnu)' = ...?

Answer 2

so I know that the start of it is 6/x but I don't know how to do the rest

Answer 3

At least you know the formula, do you?

Answer 4

I started out with this Let f(x)=ln[(x^6)(x+3)^8 ((x^2)+7)^6] and then I got it down to
6ln(x)+8ln(x+3)-6ln((x^2)+7) but then I didn't know how to get it down any further.
I just knew that the derivative of 6ln(x) would be 6/x

Answer 5

f(x)= ln[ (x^6) (x+3)^8 ((x^2) +7)^6 ]
So the question is find
f'(x) ?

Answer 6

In your original, was there division after the ^8 term?

Answer 7

no there wasn't a division

Answer 8

here's a picture if that would help

Answer 9

Hmm I'm not quite sure why you're subtracting the last log then, if there wasn't division :o

Answer 10

( ln U )' = U' / U
U' = 6x^5 * (x+3)^8 * (x²+7)^6
+ (x^6) * 8 (x+3)^7 * (x²+7)^6
+ 6x^5 * (x+3)^8 * 6(x²+7)^5 * 2x

Answer 11

Now all you do is simplify U', then plug in U'/ U

Answer 12

@AJW99 Please post the original questions, always!