Question

Найти производную функции √2x-1*(x^5+8)​

Answer 1

Ответ:

$y=\sqrt{2x-1}\cdot (x^5+8)\ \ ,\qquad \qquad \boxed{\ (uv)'=u'v+uv'\ }\\\\\\\boxed{\ (\sqrt{u})'=\dfrac{1}{2\sqrt{u}}\cdot u'\ \ ,\ \ (x^{n})'=n\cdot x^{n-1}\ }\\\\\\y'=(\sqrt{2x-1})'\cdot (x^5+8)+(x^5+8)'\cdot \sqrt{2x-1}=\\\\=\dfrac{1}{2\sqrt{2x-1}}\cdot \underbrace{(2x-1)'}_{=\, 2}\cdot (x^5+8)+\sqrt{2x-1}\cdot 5x^4=\dfrac{x^5+8}{\sqrt{2x-1}}+5x^4\cdot \sqrt{2x-1}$