Question

найти производную функции: у=х*на корень из (4-х)

Answer 1

y=x*√(4-x)

y'=x'*√(4-x)+x*√(4-x)'=√(4-x)-x/2√(4-x)=(8-3x)/(2√(4-x))

 

Answer 2

 

$<var>y = x\sqrt{4-x}\\\\ y' = (x\sqrt{4-x})' = x' \sqrt{4-x} + x(\sqrt{4-x})' = \sqrt{4-x} - x\frac{1}{2\sqrt{4-x}} =\\\\\frac{8-2x}{2\sqrt{4-x}} - x\frac{1}{2\sqrt{4-x}} = \frac{8-2x- x}{2\sqrt{4-x}} = \frac{8-3x}{2\sqrt{4-x}} </var>$