What is the derivative of y=log_x 3?

2 Answers
Oct 18, 2015

y'=-1/(xln3(log_3x)^2)

Explanation:

y=log_x3=1/log_3x = (log_3x)^-1

y'=-(log_3x)^-2*1/(xln3)

y'=-1/(xln3(log_3x)^2)

Nov 16, 2015

y'=-ln3/(x(lnx)^2

Explanation:

log_x3=ln3/lnx through the change of base formula.
d/(dx)[ln3/lnx]=ln3d/(dx)[1/lnx]=ln3color(blue)(d/(dx)[(lnx)^-1]

About to use the Chain Rule:
color(blue)(d/(dx)[(lnx)^-1])=-(lnx)^-2d/(dx)[lnx]=-1/(lnx)^2(1/x)
y'=-ln3/(x(lnx)^2