1) y = (x² - 1)(x³ + x)
y ' = (x² - 1)' * (x³ + x ) + (x² - 1) * ( x³ + x)' = 2x(x³ + x) + (x² - 1)(3x² + 1) =
= 2x⁴ + 2x² + 3x⁴ + x² - 3x² - 1 = 5x⁴ - 1
2)
![y=\frac{2 x^{2} +1}{ x^{2} -1}\\\\y'= \frac{(2 x^{2} +1)'*( x^{2} -1)-(2 x^{2} +1)( x^{2} -1)'}{ (x^{2} -1) ^{2} } = \frac{4x( x^{2} -1)-2x(2 x^{2} +1)}{( x^{2} -1) ^{2} }=](https://tex.z-dn.net/?f=+y%3D%5Cfrac%7B2+x%5E%7B2%7D+%2B1%7D%7B+x%5E%7B2%7D+-1%7D%5C%5C%5C%5Cy%27%3D+%5Cfrac%7B%282+x%5E%7B2%7D+%2B1%29%27%2A%28+x%5E%7B2%7D+-1%29-%282+x%5E%7B2%7D+%2B1%29%28+x%5E%7B2%7D+-1%29%27%7D%7B+%28x%5E%7B2%7D+-1%29+%5E%7B2%7D+%7D+%3D+%5Cfrac%7B4x%28+x%5E%7B2%7D+-1%29-2x%282+x%5E%7B2%7D+%2B1%29%7D%7B%28+x%5E%7B2%7D+-1%29+%5E%7B2%7D+%7D%3D+++)
![\frac{4 x^{3} -4x-4 x^{3}-2x }{( x^{2} -1) ^{2} }= -\frac{6x}{( x^{2} -1) ^{2} }](https://tex.z-dn.net/?f=+%5Cfrac%7B4+x%5E%7B3%7D+-4x-4+x%5E%7B3%7D-2x+%7D%7B%28+x%5E%7B2%7D+-1%29+%5E%7B2%7D+%7D%3D+-%5Cfrac%7B6x%7D%7B%28+x%5E%7B2%7D+-1%29+%5E%7B2%7D+%7D++)
3)
![y= \frac{x-1}{x+1} + \frac{x+1}{x-1} = \frac{(x-1) ^{2} +(x+1) ^{2} }{ x^{2} -1} = \frac{ x^{2} -2x+1+ x^{2}+2x+1 }{ x^{2} -1} = \frac{2 x^{2} +2}{ x^{2} -1}\\\\y'= \frac{(2 x^{2} +2)'*( x^{2} -1)-(2 x^{2} +2)*( x^{2} -1)'}{( x^{2} -1) ^{2} }= \frac{4x( x^{2} -1)-2x(2 x^{2} +2)}{( x^{2} -1) ^{2} } =](https://tex.z-dn.net/?f=y%3D+%5Cfrac%7Bx-1%7D%7Bx%2B1%7D+%2B+%5Cfrac%7Bx%2B1%7D%7Bx-1%7D+%3D+%5Cfrac%7B%28x-1%29+%5E%7B2%7D+%2B%28x%2B1%29+%5E%7B2%7D+%7D%7B+x%5E%7B2%7D+-1%7D+%3D+%5Cfrac%7B+x%5E%7B2%7D+-2x%2B1%2B+x%5E%7B2%7D%2B2x%2B1+%7D%7B+x%5E%7B2%7D+-1%7D+%3D+%5Cfrac%7B2+x%5E%7B2%7D+%2B2%7D%7B+x%5E%7B2%7D+-1%7D%5C%5C%5C%5Cy%27%3D+%5Cfrac%7B%282+x%5E%7B2%7D+%2B2%29%27%2A%28+x%5E%7B2%7D+-1%29-%282+x%5E%7B2%7D+%2B2%29%2A%28+x%5E%7B2%7D+-1%29%27%7D%7B%28+x%5E%7B2%7D+-1%29+%5E%7B2%7D+%7D%3D+%5Cfrac%7B4x%28+x%5E%7B2%7D+-1%29-2x%282+x%5E%7B2%7D+%2B2%29%7D%7B%28+x%5E%7B2%7D+-1%29+%5E%7B2%7D+%7D+%3D++++)
![\frac{4 x^{3}-4x-4 x^{3} -4x }{( x^{2} -1) ^{2} } =- \frac{8x}{( x^{2} -1) ^{2} }](https://tex.z-dn.net/?f=+%5Cfrac%7B4+x%5E%7B3%7D-4x-4+x%5E%7B3%7D+-4x+%7D%7B%28+x%5E%7B2%7D+-1%29+%5E%7B2%7D+%7D+%3D-+%5Cfrac%7B8x%7D%7B%28+x%5E%7B2%7D+-1%29+%5E%7B2%7D+%7D+)
Ответ:
Объяснение:
Первое число равно, заносим под корень 6*2=12
Второе равно (рисунок).
Третье равно, заносим под корень 4*3=12.
Четвертое тоже нет.
В числителе сумма синусов.
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