Question

Find the slope of the tangent line to f(x) at x=3.

Answer 1

\[f(x) = x ^{\frac{ 3 }{ x }}\]

Answer 2

I think it's 1- ln(3).

Answer 3

first take log of both sides and then differentiate and then substitute for x=3

Answer 4

ln f(x)=3/x lnx and then proceed ..

Answer 5

right, 1/f(x) * f'(x) = -3lnx/x^2+3/x^2 = (3(1-lnx))/x^2

f'(x) = x^(3/x)(3(1-lnx))/x^2

Answer 6

When I plug in 3, I got 1-ln3

Answer 7

or f'(x) =f(x) (-3(lnx)/(x^2) +3/(x^2))=f(x)(3/(x^2)(-lnx +1)
i hope u can do the rest

Answer 8

I was just making sure I got the right answer, but essentially, that's what I did.

Answer 9

yup ..

f'(3) =(f(3))(1/3)(1-ln3)

Answer 10

:)

Answer 11

Thanks!

Answer 12

welcome...