- #1

diffusion

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- 0

## Homework Statement

Find the following derivatives:

[tex]\frac{d}{dx}[/tex] (tanx)^(1/x)

[tex]\frac{d}{dx}[/tex] [tex]\sqrt{\frac{x-1}{x^2 (x-4)}}[/tex]

## Homework Equations

Rules of differentiation

## The Attempt at a Solution

I realize these are fairly elementary problems, just not sure the order I should perform the differentiation rules. My attempt at number 1 is as follows:

Considering 1/x as a separate function (u), we can use the chain rule:

[tex]\frac{d}{dx}[/tex]tan(x)[tex]_{u}[/tex] [tex]\frac{d}{dx}[/tex] [tex]\frac{1}{x}[/tex]

Apply quotient rule on 1/x:

= sec[tex]_{2}[/tex] (x)[tex]_{u}[/tex] [tex]\frac{1}{x^2}[/tex]

= [tex]\frac{sec^2(x) ^{1/x}}{x^2}[/tex]

Can someone please correct me if I have made any mistakes?

The second problem I'm not sure. As far as I can tell it's just applying the quotient rule to the fraction, all to the power of [tex]\frac{1}{2}[/tex]. Do I need to apply the chain rule to the denominator before using the quotient rule?