Question

Y=корень из х*(1+sin x) в 10 степени

Answer 1

$y = \sqrt{x* (1+sinx)^{10} }$

$y' = ( \sqrt{x* (1+sinx)^{10} } )' = \frac{1}{2\sqrt{x* (1+sinx)^{10} }} *(x* (1+sinx)^{10})' =$
$= \frac{1}{2\sqrt{x* (1+sinx)^{10} }} *(x'* (1+sinx)^{10}+x* (1+sinx)^{10})' )=$
$= \frac{1}{2\sqrt{x* (1+sinx)^{10} }} *( (1+sinx)^{10}+x* 10(1+sinx)^{9}*(1+sinx)' )=$
$= \frac{1}{2\sqrt{x* (1+sinx)^{10} }} *( (1+sinx)^{10}+x* 10(1+sinx)^{9}*cosx )=$
$= \frac{(1+sinx)^{10}+10(1+sinx)^{9}xcosx}{2\sqrt{x* (1+sinx)^{10} }}$

Answer 2

To make sure I understand your expression correctly, I assume you want to write the equation as follows:

$Y = \sqrt[10]{x \cdot (1 + \sin(x))}$

This equation represents $Y$ as the tenth root of the product of $x$ and $(1 + \sin(x))$.

If you have any specific questions about this equation or if you'd like me to perform any calculations or analyze its properties, feel free to let me know!