Please help me find the derivatives of the following:

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

Remenciements d'avance! :)

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]

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}

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