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По формуле производная частного ( дроби):
![(frac{u}{v})`= frac{u`cdot v- u cdot v`}{v ^{2} } (frac{u}{v})`= frac{u`cdot v- u cdot v`}{v ^{2} }](https://tex.z-dn.net/?f=+%28frac%7Bu%7D%7Bv%7D%29%60%3D+frac%7Bu%60cdot+v-+u+cdot+v%60%7D%7Bv+%5E%7B2%7D+%7D++)
![(frac{ x^{2} -2}{x+3})`= frac{( x^{2} -2)`cdot (x+3)- ( x^{2} -2) cdot (x+3)`}{(x+3) ^{2} }= (frac{ x^{2} -2}{x+3})`= frac{( x^{2} -2)`cdot (x+3)- ( x^{2} -2) cdot (x+3)`}{(x+3) ^{2} }=](https://tex.z-dn.net/?f=%28frac%7B+x%5E%7B2%7D+-2%7D%7Bx%2B3%7D%29%60%3D+frac%7B%28+x%5E%7B2%7D+-2%29%60cdot+%28x%2B3%29-+%28+x%5E%7B2%7D+-2%29+cdot+%28x%2B3%29%60%7D%7B%28x%2B3%29+%5E%7B2%7D+%7D%3D+)
![=frac{( 2x)cdot (x+3)- ( x^{2} -2) cdot 1}{(x+3) ^{2} }= frac{2 x^{2} +6x- x^{2} +2}{(x+3) ^{2} }= frac{ x^{2} +6x+2}{(x+3) ^{2} } =frac{( 2x)cdot (x+3)- ( x^{2} -2) cdot 1}{(x+3) ^{2} }= frac{2 x^{2} +6x- x^{2} +2}{(x+3) ^{2} }= frac{ x^{2} +6x+2}{(x+3) ^{2} }](https://tex.z-dn.net/?f=%3Dfrac%7B%28+2x%29cdot+%28x%2B3%29-+%28+x%5E%7B2%7D+-2%29+cdot+1%7D%7B%28x%2B3%29+%5E%7B2%7D+%7D%3D+frac%7B2+x%5E%7B2%7D+%2B6x-++x%5E%7B2%7D+%2B2%7D%7B%28x%2B3%29+%5E%7B2%7D+%7D%3D+frac%7B+x%5E%7B2%7D+%2B6x%2B2%7D%7B%28x%2B3%29+%5E%7B2%7D+%7D)
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