## bmelyk 2 years ago does y' of ln(4^s) = 1/4^s or s/4 ??

1. CliffSedge

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

2. bmelyk

so it would be s/4 then.

3. CliffSedge

ln(4) is a constant

4. bmelyk

yes but the derivative of ln=1/x

5. CliffSedge

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

6. CliffSedge

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

7. CliffSedge

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

8. bmelyk

what is c*s ???

9. bmelyk

10. TuringTest

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

11. bmelyk

umm s'?

12. TuringTest

no, what is d/dx(x) ?

13. CliffSedge

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

14. bmelyk

=1

15. TuringTest

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

16. bmelyk

=1 !

17. TuringTest

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

18. bmelyk

c

19. TuringTest

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

20. bmelyk

ln4?

21. TuringTest

yes

22. bmelyk

23. TuringTest

yep

24. CliffSedge

Thanks for the backup, Turing!

25. TuringTest

No prob!