Question

Как решить это производную ?
2x^3 делить на x^2+2x

Answer 1

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Answer 2

$(\frac{u}{v})'=\frac{u'*v-u*v'}{v^2}\\\\ (\frac{2x^3}{x^2+2x})'=(\frac{2*x*x^2}{x*(x+2)})'=(\frac{2x^2}{x+2})'=\\\\ =\frac{[2x^2]'*(x+2)-2x^2*[x+2]'}{(x+2)^2}=\\\\ =\frac{2*[x^2]'*(x+2)-2x^2*([x]'+[2]')}{(x+2)^2}=\\\\ =\frac{2*[2*x^{2-1}]*(x+2)-2x^2*([1]+[0])}{(x+2)^2}=\\\\ =\frac{4x*(x+2)-2x^2*1}{(x+2)^2}=\\\\ =\frac{4x^2+8x-2x^2}{(x+2)^2}=\\\\ =\frac{2x^2+8x}{(x+2)^2}$