Question

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

Answer 1

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