Question

Найдите f"(x) и f"(4/5), если f(x)=2lnx-1

Answer 1

$f(x)=2ln(x)-1\\\\f'(ln(x))=\frac{1}{x}\\\\f'(x)=2*\frac{1}{x}=\frac{2}{x}\\\\f'(x)=2*x^{-1}\\\\\\f''(x)=-2*x^{-2}=-\frac{2}{x^2}\\\\f''(\frac{4}{5})=-\frac{2}{(\frac{4}{5})^2}=-\frac{2}{\frac{16}{25} }=-\frac{25}{8}=-3\frac{1}{8}$