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akotoh · Aug 22, 2009, 04:06 PM

Please help me find the derivatives of the following:

1.) log(3/x)
2.) ln cot 1/2 x

Remenciements d'avance! :)

galactus · Aug 22, 2009, 05:03 PM

2.) ln cot 1/2 x

Chain rule. Derivative of inside times derivative of outside.

The derivative of ln(u)=1/u. Since u=cot(x/2), then we have $\frac{1}{2}cot(\frac{x}{2})$

Derivative of inside is the derivative of $cot(\frac{x}{2})=\frac{-1}{2}csc^{2}(\frac{x}{2})$

Multiply them and simplify:

$\frac{1}{cot(\frac{x}{2})}\cdot \frac{-1}{2}csc^{2}(\frac{x}{2})$

$=\frac{-1}{2sin(\frac{x}{2})cos(\frac{x}{2})}$

Remenciements d'avance! :)[/QUOTE]

radiation · Aug 24, 2009, 07:16 AM

Originally Posted by galactus

Chain rule. Derivative of inside times derivative of outside.

The derivative of ln(u)=1/u. Since u=cot(x/2), then we have $\frac{1}{2}cot(\frac{x}{2})$

Derivative of inside is the derivative of $cot(\frac{x}{2})=\frac{-1}{2}csc^{2}(\frac{x}{2})$

Multiply them and simplify:

$\frac{1}{cot(\frac{x}{2})}\cdot \frac{-1}{2}csc^{2}(\frac{x}{2})$

$=\frac{-1}{2sin(\frac{x}{2})cos(\frac{x}{2})}$

Remenciements d'avance! :)

[/QUOTE]

it can further be reduced to -1/sin(x) =-csc(x)
{2 sinAcosA = sin 2A}

Unknown008 · Aug 24, 2009, 12:11 PM

Of course radiation. If further simplification was required, then that would be the OP's work. :)