На координатной плоскости нет ни одной точки, принадлежащих одновременно двум из этих прямых, т.к. у прямых равные коэфициенты пропорциональности (k=3), следовательно они параллельны между собой, а значит не пересекаются.
( x - 5 )( x + 3 ) = x² + 3x - 5x - 15 = x² - 2x - 15
Ответ y = x² - 2x - 15
3x³-3y³+5x²-5y²=
=3(x-y)(x²+xy+y²)+5(x-y)(x+y)=
=(x-y)(3(x²+xy+y²)+5(x+y))
Раскрываем скобки получится:
х-3·х-7-6х²-10х=-6х²-9х-10
б) 4а(а-2)-(а-4)=4а²-8а-а+4=4а²-9а+4
в)2(m+1)²-4m=2·m²+2m+1=2m²+2m+1
![y=x^a \\ y'=a*x^{a-1} \\ \\ example; \\ y=2x^3 \\ y'=2*3x^{3-1}=6x^2 \\ ============================ \\ \\ y=3 \sqrt{x} =3x^{ \frac{1}{2} } \\ y'= 3*\frac{1}{2} x^{ \frac{1}{2}-1 }= \frac{3}{2} x^{- \frac{1}{2} }= \frac{3}{2x^{ \frac{1}{2} }} = \frac{3}{2 \sqrt{x} } \\ ============================ \\ \\ y=7x \\ y'=7*1x^{1-1}=7*1x^0=7*1*1=7](https://tex.z-dn.net/?f=y%3Dx%5Ea+%5C%5C+y%27%3Da%2Ax%5E%7Ba-1%7D+%5C%5C++%5C%5C+example%3B+%5C%5C+y%3D2x%5E3+%5C%5C+y%27%3D2%2A3x%5E%7B3-1%7D%3D6x%5E2+%5C%5C+%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D+%5C%5C++%5C%5C+y%3D3+%5Csqrt%7Bx%7D+%3D3x%5E%7B+%5Cfrac%7B1%7D%7B2%7D+%7D+%5C%5C+y%27%3D+3%2A%5Cfrac%7B1%7D%7B2%7D+x%5E%7B+%5Cfrac%7B1%7D%7B2%7D-1+%7D%3D+%5Cfrac%7B3%7D%7B2%7D+x%5E%7B-+%5Cfrac%7B1%7D%7B2%7D+%7D%3D+%5Cfrac%7B3%7D%7B2x%5E%7B+%5Cfrac%7B1%7D%7B2%7D+%7D%7D+%3D+%5Cfrac%7B3%7D%7B2+%5Csqrt%7Bx%7D+%7D++%5C%5C+%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D+%5C%5C++%5C%5C+y%3D7x+%5C%5C+y%27%3D7%2A1x%5E%7B1-1%7D%3D7%2A1x%5E0%3D7%2A1%2A1%3D7)
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а)
![y'=2x-7](https://tex.z-dn.net/?f=y%27%3D2x-7)
б)
![y'= \frac{1}{2 \sqrt{x} } -18x](https://tex.z-dn.net/?f=y%27%3D+%5Cfrac%7B1%7D%7B2+%5Csqrt%7Bx%7D+%7D+-18x)
в)
![y'=14x+3](https://tex.z-dn.net/?f=y%27%3D14x%2B3)
г)
![y'= \frac{1}{2 \sqrt{x} } -10x](https://tex.z-dn.net/?f=y%27%3D+%5Cfrac%7B1%7D%7B2+%5Csqrt%7Bx%7D+%7D+-10x)