Question

differentiate. [ln(x)]/[1+ln(2x)] please show steps

Answer 1

Quotient rule says d/dx(f(x)/g(x)) = (f'(x)g(x)-g'(x)f(x))/(g(x))^2
Or more simply, (the derivative of the top times the bottom) minus (the derivative of the bottom times the top) all over the bottom squared.

(1/x) = derivative of ln(x)

(1/x)(1+ln2x)-(1/2x)(lnx)
---------------------
(1+ln2x)^2

Answer 2

i dont use chain rule on the bottom?

Answer 3

The bottom is just squared, you don't take the derivative of the bottom.

Answer 4

oh, right. isnt the derivative of 1+ln2x = 2/2x?

Answer 5

Yeah, you're right the derivative of ln(2x) is 2/2x due to the chain rule, whoops.

Answer 6

alrite cool. thamks dude.