# Derivative HELP!!

• Oct 1st 2012, 04:20 PM
pnfuller
Derivative HELP!!
use logarithmic differentiation to find the derivative of the function:

y=(tanx)1/x

the answer is (tanx)1/x(sec2x/xtanx - lntanx/x2)

but how did they get to that answer i dont understand?
• Oct 1st 2012, 04:55 PM
pickslides
Re: Derivative HELP!!
What have you tried?

start by taking the log of both sides. Use the fact that $\log_ab^c = c \log_ab$

Logarithmic Differentiation
• Oct 1st 2012, 05:00 PM
Soroban
Re: Derivative HELP!!
Hello, pnfuller!

Quote:

Use logarithmic differentiation to find the derivative of the function:

. . $y\:=\:(\tan x)^{\frac{1}{x}}$
Answer: . $y' \;=\;(\tan x)^{\frac{1}{x}}\left[\frac{\sec^2x}{x\tan x} - \frac{\ln(\tan x)}{x^2}\right]$

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 PM
pnfuller
Re: Derivative HELP!!
i have not done logarithmic differentiation so i dont know where to start?
Quote:

Originally Posted by Soroban
Hello, pnfuller!

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, 05:41 PM
Prove It
Re: Derivative HELP!!
Quote:

Originally Posted by pnfuller
i have not done logarithmic differentiation so i dont know where to start?

Then have you done implicit differentiation before? If so, that makes things a lot easier. If not, you need to use the chain rule after a transformation.