Question

Найти производную f(x)=sinx/ln(2x)+x+1, при x=Pi/2

Answer 1

$f(x)=\frac{sinx}{ln2x}+x+1\\\\f'(x)=\frac{cosx\cdot ln2x-sinx\cdot \frac{2}{2x}}{ln^22x}+1=\frac{x\cdot cosx\cdot ln2x-sinx}{x\cdot ln^22x}+1\\\\f'(\frac{\pi}{2})=\frac{0-1}{\frac{\pi}{2}\cdot ln^2\pi }+1=-\frac{2}{\pi \cdot ln^2\pi }+1$