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?

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- Oct 1st 2012, 04:20 PMpnfullerDerivative HELP!!
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? - Oct 1st 2012, 04:55 PMpickslidesRe: Derivative HELP!!
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 - Oct 1st 2012, 05:00 PMSorobanRe: Derivative HELP!!
Hello, pnfuller!

Quote:

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.

- Oct 1st 2012, 05:06 PMpnfullerRe: Derivative HELP!!
- Oct 1st 2012, 05:41 PMProve ItRe: Derivative HELP!!