Question

Найти производную функции y=(x^9)^x

Answer 1

$\y=(x^9)^x\ y=x^{9x}\ y=e^{ln x^{9x}}\ y=e^{9x ln x}\ y'=e^{9x ln x}(9ln x+9xcdotfrac{1}{x})\ y'=9x^{9x}(ln x+1)$

Answer 2

lny=xlnx^9=x*9lnx

(lny)'=9(lnx+x/x)=y'/y

y'=9y(lnx+1)=9((x^9)^x)*ln(e*x)