Question

Найти производную

1/2 * log(e^(2*x) + 1) - 2*arctg(e^x)

Answer 1

$y=frac{1}{2}ln(e^{2x}+1)-2arctge^{x}\\y'=frac{1}{2}cdot frac{2e^{2x}}{e^{2x}+1}-frac{2e^{x}}{1+e^{2x}}=frac{2e^{x}}{e^{2x}+1}cdot left (frac{1}{2}cdot e^{x}-1right )$