Question

найти пройзводную
3^3корень из x+2/x^2-2x^3+3

Answer 1

если так выглядит

$frac{3^{3}sqrt{x+2}}{x^{2}-2x^{3}+3}$, то

($frac{3^{3}sqrt{x+2}}{x^{2}-2x^{3}+3}$)'=$frac{(3^{3}sqrt{x+2})'*(x^{2}-2x^{3}+3)-(3^{3}sqrt{x+2})*(x^{2}-2x^{3}+3)'}{(x^{2}-2x^{3}+3)^2}$=$frac{27xfrac{1}{sqrt{x+2}}*(x^{2}-2x^{3}+3)-(3^{3}sqrt{x+2})*(2x-6x^{2})}{(x^{2}-2x^{3}+3)^2}=$$frac{frac{27x^{3}-54x^{4}+81x}{sqrt{x+2}}-(3^{3}sqrt{x+2})*(2x-6x^{2})}{(x^{2}-2x^{3}+3)^2}=$$frac{{27x^{3}-54x^{4}+81x}-sqrt{x+2}(3^{3}sqrt{x+2})*(2x-6x^{2})}{sqrt{x+2}(x^{2}-2x^{3}+3)^2}$ = $frac{{27x^{3}-54x^{4}+81x}-27(x+2)*(2x-6x^{2})}{sqrt{x+2}(x^{2}-2x^{3}+3)^2}=$ $frac{{27x^{3}-54x^{4}+81x}-27(-6x^{3}-10x^{2}+4x)}{sqrt{x+2}(x^{2}-2x^{3}+3)^2}=$$frac{{27x^{3}-54x^{4}+81x}-(-162x^{3}-270x^{2}+108x)}{sqrt{x+2}(x^{2}-2x^{3}+3)^2}$=$frac{{189x^{3}-216x^{4}-27x}}{sqrt{x+2}(x^{2}-2x^{3}+3)^2}<var></var>$