Question

calculate, using the productrule, the derivative of x (2logx)

Product rule:

(f(x) (g(x))' = f'(x) g(x) + f(x) g'(x)

f(x) = x f'(x) = 1
g(x) = 2log(x) g'(x) = ???

I think 2Log(x) = 1 / xln2

then fill in the productrule :

1 . 2log(x) + x . (1 / xln2)

= 2log(x) + x / xln2

however. the asnwer book sais it should be

(1 + ln x) / (ln2)

Answer 1

g' = 2/x

Answer 2

of course, depending on what math class you are int, log can mean base 10, or it can be a natural log ....

if base 10, then g' = 2/(xln(10))

Answer 3

I still don't get that part. It's a base 10. but why is the g' 2/x because of the 2 standing in front of the log ?

Answer 4

a few things to keep in mind:

constants pull out, and logs have a change of base process.

\[log_b(x)=\frac{ln(x)}{ln(b)}\]
1/ln(b) is just another constant.

\[2log_{10}(x)=\frac{2}{ln(10)}ln(x)\]pull out the constant and derive the ln(x)