Find the derivative.
f(x)=(1+logᴈx)/x
f'(x)=[1-ln3-logᴈx (ln3)]/(x²ln3)
How do you simplify it further? Thanks.
4 answers
Whatn is the ᴈ symbol supposed to represent? Why do you have both ln and log terms? Do they have the same base?
I would change the log3x to
lnx/ln3
then y = (1 + lnx/ln3)/x
= 1/x + lnx/(ln3x)
dy/dx = -1/x^2 + [(ln3)x((1/x) - x(ln3)]/x^2
= -1/x^2 + [(ln3)x(1/x) - (lnx)(ln3)]/((ln3)^2(x^2))
leaving any further simplification up to you
lnx/ln3
then y = (1 + lnx/ln3)/x
= 1/x + lnx/(ln3x)
dy/dx = -1/x^2 + [(ln3)x((1/x) - x(ln3)]/x^2
= -1/x^2 + [(ln3)x(1/x) - (lnx)(ln3)]/((ln3)^2(x^2))
leaving any further simplification up to you
sh: Your "subscript 3 symbol" showed up as a square on my computer. Hence the confusion.
I understand now, thanks! I changed the log to, 1/xln3 instead.
5 answers