- #1

SYoungblood

- 64

- 1

## Homework Statement

Hello, I had a few derivative of the natural logarithm functions questions. It seems like it should be fairly straightforward, but I am turning it into a pig’s ear.On my honor, none of these are problems on an assessment per se, however, they are not materially different than anything that I am finding in my calc book and what I would assume to be on a midterm or final:## Homework Equations

[/B]

a) ln 3x

b) ln 3x + x

c) ln (3x + 4)

d) ln (x^2)

e) ln x^2

f) x (ln 2x)^4

## The Attempt at a Solution

a) I believe I got this right – 1/3x

b) I think I have this one as well – 1/3x + 1

c) I have (3x + 4)’/(3x + 4) = 3/(3x + 4)

d) Using the chain rule, I believe this is 2x/x^2

e) I believe using the ln x derivative rules, this is 2 (ln x)’ = 2/x

f) This is giving me problems. Using the product rule and chain rule, I think the answer

= 1 * (ln 2x)^4 + x * 4(ln 2x)^3 * 1/2x

= (ln2x)^4 + 4 [(ln 2x)^3]/x, with an x in the numerator and denominator in the final term cancelling each other out.

Thank you for your help --

SY