Question

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

Answer 1

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