Ответ:
Объяснение:
17.
1) y'=((x³-2)(x²+1))'=3x²*(x²+1)+(x³-2)*2x=3x⁴+3x²+2x⁴-4x=
=5x⁴+3x²-4x=x*(5x³+3x-4).
![2)y'=(\sqrt{x}*(3x^{2}-2))'= \frac{3x^{2} -2}{2*\sqrt{x}} +\sqrt{x} *6x=\frac{3x^{2}-2+2\sqrt{x}*\sqrt{x}*6 }{2\sqrt{x} } =\\ =\frac{3x^{2} -2+12x^{2} }{2\sqrt{x} } =\frac{15x^{2}-2 }{2\sqrt{x} } 2)y'=(\sqrt{x}*(3x^{2}-2))'= \frac{3x^{2} -2}{2*\sqrt{x}} +\sqrt{x} *6x=\frac{3x^{2}-2+2\sqrt{x}*\sqrt{x}*6 }{2\sqrt{x} } =\\ =\frac{3x^{2} -2+12x^{2} }{2\sqrt{x} } =\frac{15x^{2}-2 }{2\sqrt{x} }](https://tex.z-dn.net/?f=2%29y%27%3D%28%5Csqrt%7Bx%7D%2A%283x%5E%7B2%7D-2%29%29%27%3D%20%20%5Cfrac%7B3x%5E%7B2%7D%20-2%7D%7B2%2A%5Csqrt%7Bx%7D%7D%20%2B%5Csqrt%7Bx%7D%20%2A6x%3D%5Cfrac%7B3x%5E%7B2%7D-2%2B2%5Csqrt%7Bx%7D%2A%5Csqrt%7Bx%7D%2A6%20%20%20%7D%7B2%5Csqrt%7Bx%7D%20%7D%20%3D%5C%5C%20%3D%5Cfrac%7B3x%5E%7B2%7D%20-2%2B12x%5E%7B2%7D%20%7D%7B2%5Csqrt%7Bx%7D%20%7D%20%3D%5Cfrac%7B15x%5E%7B2%7D-2%20%7D%7B2%5Csqrt%7Bx%7D%20%7D)
![3)y'=((\sqrt{x} +1)(3-2\sqrt{x} ))'=\frac{3-2\sqrt{x} }{2\sqrt{x} } +\frac{\sqrt{x}+1 }{-\sqrt{x} } =\frac{3-2\sqrt{x}-2\sqrt{x} -2 }{2\sqrt{x} } =\frac{1-4\sqrt{x} }{2\sqrt{x} } =\frac{1}{2\sqrt{x} } -2 3)y'=((\sqrt{x} +1)(3-2\sqrt{x} ))'=\frac{3-2\sqrt{x} }{2\sqrt{x} } +\frac{\sqrt{x}+1 }{-\sqrt{x} } =\frac{3-2\sqrt{x}-2\sqrt{x} -2 }{2\sqrt{x} } =\frac{1-4\sqrt{x} }{2\sqrt{x} } =\frac{1}{2\sqrt{x} } -2](https://tex.z-dn.net/?f=3%29y%27%3D%28%28%5Csqrt%7Bx%7D%20%2B1%29%283-2%5Csqrt%7Bx%7D%20%29%29%27%3D%5Cfrac%7B3-2%5Csqrt%7Bx%7D%20%7D%7B2%5Csqrt%7Bx%7D%20%7D%20%2B%5Cfrac%7B%5Csqrt%7Bx%7D%2B1%20%7D%7B-%5Csqrt%7Bx%7D%20%7D%20%3D%5Cfrac%7B3-2%5Csqrt%7Bx%7D-2%5Csqrt%7Bx%7D%20-2%20%7D%7B2%5Csqrt%7Bx%7D%20%7D%20%3D%5Cfrac%7B1-4%5Csqrt%7Bx%7D%20%7D%7B2%5Csqrt%7Bx%7D%20%7D%20%3D%5Cfrac%7B1%7D%7B2%5Csqrt%7Bx%7D%20%7D%20-2)
4) y'=(x²*sin(x))'=2x*sin(x)+x²*cos(x)=x*(2*sin(x)+x*cos(x)).
5) y'=((x²-3x+1)*(x⁴-3x+2))'=(2x-3)*(x⁴-3x+2)+(x²-3x+1)*(4x³-3)=
=2x⁵-6x²+4x-3x⁴+22x9x-6+4x⁵-12x⁴+4x³-3x²+9x-3=6x⁵-15x⁴+4x³-9x²+22x-9
![6)y'=(3x*tg(x))'=3*tg(x)+\frac{3x}{cos^{2}(x) } =3*(tg(x)+x*sec(x)). 6)y'=(3x*tg(x))'=3*tg(x)+\frac{3x}{cos^{2}(x) } =3*(tg(x)+x*sec(x)).](https://tex.z-dn.net/?f=6%29y%27%3D%283x%2Atg%28x%29%29%27%3D3%2Atg%28x%29%2B%5Cfrac%7B3x%7D%7Bcos%5E%7B2%7D%28x%29%20%7D%20%3D3%2A%28tg%28x%29%2Bx%2Asec%28x%29%29.)
18.