Question

Differentiate f(x)=logax.

Answer 1

\[f(x)=\log _{a}X\]

Answer 2

i think its 1/x but that is not right

Answer 3

use the property of log
\(\huge\log_ab=\frac{\ln b}{\ln a}\)

Answer 4

then differentiate

Answer 5

\[\log_{a} x = \frac{\ln x}{\ln a}\]

Note that ln a is constant.

Answer 6

remember that a is constant

Answer 7

Do you know the derivative of ln x?

Answer 8

@Brooke_army are u getting, whats is going on ?

Answer 9

yes sort of

Answer 10

so what would be your answer ?

Answer 11

i have no idea

Answer 12

how do you fine the derivative of ln x?

Answer 13

its pretty standard
its 1/x

Answer 14

now ?

Answer 15

is it a/x?

Answer 16

umm.. nopes
since ln a is constant, you can write
f'(x) = (log_a x )' = ( ln x/ ln a)' = (1/ln a) (ln x)'
and (ln x)'=1/x

Answer 17

ok?

Answer 18

yes that makes sense now. Thanks for the help

Answer 19

finally its 1/ (x ln a).
welcome ^_^