use logarithmic differentiation to find the derivative of the function:
y=(tanx)^{1/x}
the answer is (tanx)^{1/x}(sec^{2}x/xtanx - lntanx/x^{2})
but how did they get to that answer i dont understand?
What have you tried?
start by taking the log of both sides. Use the fact that $\displaystyle \log_ab^c = c \log_ab$
Good reading is here
Logarithmic Differentiation
Hello, pnfuller!
Use logarithmic differentiation to find the derivative of the function:
. . $\displaystyle y\:=\:(\tan x)^{\frac{1}{x}}$
Answer: .$\displaystyle y' \;=\;(\tan x)^{\frac{1}{x}}\left[\frac{\sec^2x}{x\tan x} - \frac{\ln(\tan x)}{x^2}\right]$
but how did they get to that answer . . . i dont understand?
What part don't you understand?
What did you get for your answer? .And how did you get it?
Have you EVER done any logarithmic differentiation?
If not, you need more help than we can offer.