Question

Use logarithmic differentiation to find the derivative of the function

y=x^(1/x)

Answer 1

not sure how to take derivative of (1/x)lnx

Answer 2

\[ \ln(x^\frac{1}{x}) = \frac{\ln(x)}{x} \]

Answer 3

You can use quotient rule.

Answer 4

use the product rule for (1/x) ln x

Answer 5

-1x^-2(lnx)+x^-1(1/x)

Answer 6

yes - quotient rule will do it also

Answer 7

\[ \frac{d}{dx}\frac{f}{g} =\frac{ f'g-fg'}{g^2}\]

Answer 8

did i do the product rule right?

Answer 9

oh. got it. thanks

Answer 10

yes