Question

does y' of ln(4^s) = 1/4^s or s/4 ??

Answer 1

\(\large ln(4^s) = s \cdot ln(4)\)

Answer 2

so it would be s/4 then.

Answer 3

ln(4) is a constant

Answer 4

yes but the derivative of ln=1/x

Answer 5

If you are finding \(\large y'=\frac{d}{ds}[ ln(4^s)]\)

\(\large y'=\frac{d}{ds}[ ln(4)s] =\frac{d}{ds}[c\cdot s], \space c=ln(4)\)

Answer 6

The derivative of ln x is 1/x, but ln 4 is a constant, and the derivative of a constant is zero.

Answer 7

But here you are taking the derivative of a constant times a variable.

Answer 8

what is c*s ???

Answer 9

im confused by your explanation.

Answer 10

the derivative is with respect to s
what is d/ds(s) ?

Answer 11

umm s'?

Answer 12

no, what is d/dx(x) ?

Answer 13

s' would be if s was a function of some other variable.

Answer 14

=1

Answer 15

yes, so we just changed the name of s to x
...so d/ds(s)=?

Answer 16

=1 !

Answer 17

yes :)
now what if we multiply by a constant that we call 'c' ?
then d/ds(cs)=?

Answer 18

c

Answer 19

yes
now for your problem we can write ln(4^s)=s*ln4
ln4 is a constant, so
d/ds(ln(4^s))=?

Answer 20

ln4?

Answer 21

yes

Answer 22

so thats the answer?

Answer 23

yep

Answer 24

Thanks for the backup, Turing!

Answer 25

No prob!