Question

Как найти производную функции? В чем я ошибаюсь?

Answer 1

$frac{1}{11}f'(6* sqrt[5]{ x^{9}}+9)*(6 sqrt[5]{x^9}+9)^ frac{1}{11}^-^1$
$frac{1}{11}f'(6* sqrt[5]{x^9})*(6* sqrt[5]{x^9}+9)^ frac{1}{11}^-^1$
$frac{6}{11}f'( sqrt[5]{x^9})*(6* sqrt[5]{x^9}+9)^ frac{1}{11}^-^1$
$frac{6}{55}f'(x^9)*x^9^*^(^ frac{1}{5}^-^1^)*(6* sqrt[5]{x^9}+9)^ frac{1}{11}^-^1$
$frac{54}{55}*x^9^*^(^ frac{1}{5}^-^1^)^+^8*(6* sqrt[5]{x^9})^ frac{1}{11}^-^1$
$frac{54*x^ frac{4}{5}*(6* sqrt[5]{x^9}+9)^-^ frac{10}{11}}{55}$

Answer 2

$y(x)=sqrt[11]{9+6sqrt[5]{x^9}}=left(9+6x^{tfrac{9}{5}}right)^{tfrac{1}{11}}\y'(x)=cfrac{1}{11}left(9+6x^{tfrac{9}{5}}right)^{tfrac{1}{11}-1}cdot left(9+6x^{tfrac{9}{5}}right)'=\=cfrac{1}{11}left(9+6x^{tfrac{9}{5}}right)^{-tfrac{10}{11}}cdot cfrac{6cdot 9}{5}cdot x^{tfrac{4}{5}}=\=cfrac{54}{55}cfrac{sqrt[5]{x^4}}{sqrt[11]{left(9+6sqrt[5]{x^9}right)^{10}}}$