Question

Find the derivative of y=log(4x)

Answer 1

hint :
log(4x) = ln(4x)/ln(10)

Answer 2

\[\frac{ d }{ dx }\left( \log _{a} (x)\right)=\frac{ 1 }{ xln(a) }\]

Answer 3

correct

Answer 4

yes, you used change of base

Answer 5

it is better to change base than remember this formula.
if you change base you only need to know the derivative of ln

Answer 6

yes that would be easier let me try it on paper.

Answer 7

then you used quotient rule correct?

Answer 8

no, ln(10) is just a number :)

Answer 9

you lost me

Answer 10

taking the derivative of
ln(4x)/ln(10)
is not requiring quotient rule since ln(10) is a number and hence you dont have to differentiate it

Answer 11

ok so my answer is u' over u correct?

Answer 12

ok got it,
u=4x u'=4

Answer 13

using the formula above it is
\[\frac{ 4 }{ 4x(\ln10) }\]

Answer 14

4/4 is one so my solution is 1/(x(ln10))
is your way faster

Answer 15

ok got it, I used the formula and the chain rule. My solutions match the key....

Answer 16

you can always use this formula but then you have to remember it.
i prefer to change base