Question

решите производную
(x+1)^x+1
срочно!

Answer 1

Находим по формуле:

$y' = ( ln(y) )' \times y$

$( ln(y) )' = ( ln( {(x + 1)}^{x + 1} )' = ((x + 1) ln(x + 1) )' = 1 \times ln(x + 1) + \frac{1}{x + 1} \times (x + 1) = ln(x +1 ) +1$

$y' = {(x + 1)}^{x + 1} \times (ln(x + 1)+1)$