Question

Найти производную заданной функции: y=ln arctg√(1+x^5)

Answer 1

$y'= \frac{1}{arctg \sqrt{1+x^5}}*(arctg \sqrt{1+x^5})'= \\ \frac{1}{arctg \sqrt{1+x^5}}* \frac{1}{1+(1+x^5)^2}*( \sqrt{1+x^5})'= \\ \frac{1}{arctg \sqrt{1+x^5}}* \frac{1}{(1+(1+x^5)^2}* \frac{5x^4}{2 \sqrt{1+x^5}}$