# How do you differentiate f(x)=csc5x * csc2x using the product rule?

$f = \csc 5 x , g = \csc 2 x$
$f ' = - \csc 5 x \cot 5 x \cdot 5 , g ' = - \csc 2 x \cot 2 x \cdot 2$
$f ' \left(x\right) = f g ' + g f ' = \left(\csc 5 x\right) \left(- 2 \csc 2 x \cot 2 x\right) + \left(\csc 2 x\right) \left(- 5 \csc 5 x \cot 5 x\right)$