What am I doing wrong in this derivative

[adelin]

my derivative of log4(r)*log2(r)= log2(r)/rln(4)+log4(r)/rln(2)

my book says the derivative should be 2(ln(r))/(r(ln(2))(ln(4))
what am I doing wrong?

 

[scurty]

my derivative of log4(r)*log2(r)= log2(r)/rln(4)+log4(r)/rln(2)

my book says the derivative should be 2(ln(r))/(r(ln(2))(ln(4))
what am I doing wrong?

Do you know how to convert logs to different bases?

 

[Ray Vickson]

my derivative of log4(r)*log2(r)= log2(r)/rln(4)+log4(r)/rln(2)

my book says the derivative should be 2(ln(r))/(r(ln(2))(ln(4))
what am I doing wrong?

What does log4(r) mean? Is it $\log(4r)$, log to base 4 of r, or is it $\log(r)^4$?

 

[pasmith]

my derivative of log4(r)*log2(r)= log2(r)/rln(4)+log4(r)/rln(2)

my book says the derivative should be 2(ln(r))/(r(ln(2))(ln(4))
what am I doing wrong?

You can simplify your expression further:
<br /> \frac{\log_2(r)}{r \ln 4} + \frac{\log_4(r)}{r \ln 2} = <br /> \frac{\ln r}{(r \ln 4) \ln 2} + \frac{\ln r}{(r \ln 2) \ln 4}<br /> = \frac{2 \ln r}{r \ln 2 \ln 4}<br />

 

[adelin]

1/ln(b)*1/r* dy/dx(r)