Question

Найдите производную f(x0),если f(x)=xctgx,а x0=n/4

Answer 1

$f(x)=xctgx \ f'(x)=ctgx+x* frac{-sin^2x-cosx*cosx}{sin^2x} = ctgx- frac{x}{sin^2x} \ f'( frac{pi}{4})=ctg frac{pi}{4} - frac{ frac{pi}{4} }{sin^2 frac{pi}{4} } = 1- frac{ frac{pi}{4} }{ frac{1}{2} }=1- frac{pi}{2}$