Question

y(2-5x^(2))/(2+3x)
найти произвольную.

Answer 1

$\displaystyle\bf\\y=\frac{2-5x^{2} }{2+3x} \\\\\\y'=\frac{(2-5x^{2} )'\cdot(2+3x)-(2-5x^{2} )\cdot(2+3x)'}{(2+3x)^{2} } =\\\\\\=\frac{-10x\cdot(2+3x)-(2-5x^{2} )\cdot 3}{(2+3x)^{2} }=\frac{-20x-30x^{2} -6+15x^{2} }{(2+3x)^{2} } =\\\\\\=\frac{-15x^{2} -20x-6}{(2+3x)^{2} } =-\frac{15x^{2} +20x+6}{(2+3x)^{2} }$