![(2^3 \sqrt{x^2-1}+4\sqrt{x^3-6x^2})'=2^3 (\sqrt{x^2-1})' + 4(\sqrt{x^3-6x^2})'](https://tex.z-dn.net/?f=%282%5E3+%5Csqrt%7Bx%5E2-1%7D%2B4%5Csqrt%7Bx%5E3-6x%5E2%7D%29%27%3D2%5E3+%28%5Csqrt%7Bx%5E2-1%7D%29%27+%2B+4%28%5Csqrt%7Bx%5E3-6x%5E2%7D%29%27)
Далее по правлилу производных от сложной функции:
![2^3 (\sqrt{x^2-1})' + 4(\sqrt{x^3-6x^2})'= 2^3 \frac{1}{2} \frac{(x^2-1)'}{\sqrt{x^2-1}}+ 4 \frac{1}{2} \frac{(x^3-6x^2)'}{\sqrt{x^3-6x^2}} = \newline = 2^3 \frac{1}{2} \frac{2x}{\sqrt{x^2-1}}+ 4 \frac{1}{2} \frac{3x^2-12x}{\sqrt{x^3-6x^2}} = 2^3 \frac{2x}{\sqrt{x^2-1}}+2\frac{3x^2-12x}{\sqrt{x^3-6x^2}}](https://tex.z-dn.net/?f=2%5E3+%28%5Csqrt%7Bx%5E2-1%7D%29%27+%2B+4%28%5Csqrt%7Bx%5E3-6x%5E2%7D%29%27%3D+2%5E3++%5Cfrac%7B1%7D%7B2%7D++%0A%5Cfrac%7B%28x%5E2-1%29%27%7D%7B%5Csqrt%7Bx%5E2-1%7D%7D%2B+4++%5Cfrac%7B1%7D%7B2%7D++%0A%5Cfrac%7B%28x%5E3-6x%5E2%29%27%7D%7B%5Csqrt%7Bx%5E3-6x%5E2%7D%7D+%3D+%5Cnewline%0A%3D+2%5E3++%5Cfrac%7B1%7D%7B2%7D++%5Cfrac%7B2x%7D%7B%5Csqrt%7Bx%5E2-1%7D%7D%2B+4++%5Cfrac%7B1%7D%7B2%7D++%0A%5Cfrac%7B3x%5E2-12x%7D%7B%5Csqrt%7Bx%5E3-6x%5E2%7D%7D+%3D+2%5E3+%0A%5Cfrac%7B2x%7D%7B%5Csqrt%7Bx%5E2-1%7D%7D%2B2%5Cfrac%7B3x%5E2-12x%7D%7B%5Csqrt%7Bx%5E3-6x%5E2%7D%7D)
1)cosa-sina*ctga= cos a - sin a *cos a/sin a=cosa - cos a= 0
2) cos^2a/1-sin a= 1-sin^2a/1-sin a=(1-sin a)(1+sin a) /1-sin a=1+sin a
49-9х^2 - (18x^2-16x) = 49-9х^2 - 18x^2+16x = 27x^2-16x-49
вроде так