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Old 10-07-09, 06:31 PM   #1
AchiLLe..s
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Calculus math problem

How do you do the following:

Find y' (y prime)

y=(tanx)^(1/x)

I have no clue how to do this problem
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Old 10-07-09, 06:42 PM   #2
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I think they want you to find the derivative ( ' ), ie find dy/dx if y=......
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Old 10-07-09, 07:07 PM   #3
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Take the natural log of both sides (ln). Then you can take the (1/x) down to the front of the ln(tanx). Then take the dirivative of both sides.
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Old 10-07-09, 08:23 PM   #4
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I found y'. It is in the second line of your post...
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Old 10-08-09, 05:08 PM   #5
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Quote:
Originally Posted by Hickeydog View Post
Take the natural log of both sides (ln). Then you can take the (1/x) down to the front of the ln(tanx). Then take the dirivative of both sides.
When you do this and solve for yprime, you sill may have a y somewhere in your equation. You simply substitute your origional equation for y so you have a function of x only.
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Old 10-08-09, 07:03 PM   #6
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Use the chain rule, then the quotient rule, then the chain rule again...

Just a hint:

tanx^(1/x) = exp(1/x ln tanx) and the exponential chain rule d exp(u)/du * du/dx where u = 1/x ln(tanx)
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