(у-4)в квадрате - (у+2)*8=у в квадрате-4 в квадрате-(у*8+2*8)=у в квадрате-16-8у+16=у*у - 8у
a) _________________________________
![F(x) = \sin \dfrac{\pi}2 \cdot x^2 - \cos \dfrac{\pi}2 \cdot x=1\cdot x^2-0\cdot x=x^2\\\boldsymbol{F'(x)=2x}](https://tex.z-dn.net/?f=F%28x%29%20%3D%20%5Csin%20%5Cdfrac%7B%5Cpi%7D2%20%5Ccdot%20x%5E2%20-%20%5Ccos%20%5Cdfrac%7B%5Cpi%7D2%20%5Ccdot%20x%3D1%5Ccdot%20x%5E2-0%5Ccdot%20x%3Dx%5E2%5C%5C%5Cboldsymbol%7BF%27%28x%29%3D2x%7D)
б) _________________________________
![F(x) = 2\cos \dfrac{\pi}6 \cdot \sin \dfrac{\pi}6 \cdot x^3 +\cos{\pi}\cdot x=\\\\~~~~~~~=\sin\dfrac {\pi}3\cdot x^3 -1\cdot x=\dfrac{\sqrt3}2\cdot x^3-x\\\\\boldsymbol{F'(x)=\dfrac{3\sqrt3}2\cdot x^2-1}](https://tex.z-dn.net/?f=F%28x%29%20%3D%202%5Ccos%20%5Cdfrac%7B%5Cpi%7D6%20%5Ccdot%20%5Csin%20%5Cdfrac%7B%5Cpi%7D6%20%5Ccdot%20x%5E3%20%2B%5Ccos%7B%5Cpi%7D%5Ccdot%20x%3D%5C%5C%5C%5C~~~~~~~%3D%5Csin%5Cdfrac%20%7B%5Cpi%7D3%5Ccdot%20x%5E3%20-1%5Ccdot%20x%3D%5Cdfrac%7B%5Csqrt3%7D2%5Ccdot%20x%5E3-x%5C%5C%5C%5C%5Cboldsymbol%7BF%27%28x%29%3D%5Cdfrac%7B3%5Csqrt3%7D2%5Ccdot%20x%5E2-1%7D)
в) _________________________________
![F(x) = tg\Big(-\dfrac{\pi}6\Big) \cdot x^5 - \sin^2 \dfrac{\pi}4 - 3\cos \dfrac{\pi}3\cdot x^4=\\\\~~~~~~~=-\dfrac{\sqrt3}3\cdot x^5-\dfrac 12-\dfrac 32\cdot x^4\\\\\boldsymbol{F'(x)=-\dfrac{5\sqrt3}3\cdot x^4-6\cdot x^3}](https://tex.z-dn.net/?f=F%28x%29%20%3D%20tg%5CBig%28-%5Cdfrac%7B%5Cpi%7D6%5CBig%29%20%5Ccdot%20x%5E5%20-%20%5Csin%5E2%20%5Cdfrac%7B%5Cpi%7D4%20-%203%5Ccos%20%5Cdfrac%7B%5Cpi%7D3%5Ccdot%20x%5E4%3D%5C%5C%5C%5C~~~~~~~%3D-%5Cdfrac%7B%5Csqrt3%7D3%5Ccdot%20x%5E5-%5Cdfrac%2012-%5Cdfrac%2032%5Ccdot%20x%5E4%5C%5C%5C%5C%5Cboldsymbol%7BF%27%28x%29%3D-%5Cdfrac%7B5%5Csqrt3%7D3%5Ccdot%20x%5E4-6%5Ccdot%20x%5E3%7D)
г) _________________________________
![f(x) = (2x+1)^3\\\boldsymbol{f'(x) = 3(2x+1)^2\cdot 2=6(2x+1)^2}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%282x%2B1%29%5E3%5C%5C%5Cboldsymbol%7Bf%27%28x%29%20%3D%203%282x%2B1%29%5E2%5Ccdot%202%3D6%282x%2B1%29%5E2%7D)
д) _________________________________
![F(x) = \sqrt{x^2-3}\\\\\boldsymbol{F'(x) =\dfrac{(x^2-3)'}{2\sqrt{x^2-3}}=\dfrac{x}{\sqrt{x^2-3}}}](https://tex.z-dn.net/?f=F%28x%29%20%3D%20%5Csqrt%7Bx%5E2-3%7D%5C%5C%5C%5C%5Cboldsymbol%7BF%27%28x%29%20%3D%5Cdfrac%7B%28x%5E2-3%29%27%7D%7B2%5Csqrt%7Bx%5E2-3%7D%7D%3D%5Cdfrac%7Bx%7D%7B%5Csqrt%7Bx%5E2-3%7D%7D%7D)
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В решении использованы табличные значения тригонометрических функций и формулы
![2\sin\alpha \cos \alpha =\sin(2\alpha) \\\\\Big(x^n\Big)'=n\cdot x^{n-1};~~~~~~~(const)'=0\\\\\sqrt{u}=\dfrac{u'}{2\sqrt u}](https://tex.z-dn.net/?f=2%5Csin%5Calpha%20%5Ccos%20%5Calpha%20%3D%5Csin%282%5Calpha%29%20%5C%5C%5C%5C%5CBig%28x%5En%5CBig%29%27%3Dn%5Ccdot%20x%5E%7Bn-1%7D%3B~~~~~~~%28const%29%27%3D0%5C%5C%5C%5C%5Csqrt%7Bu%7D%3D%5Cdfrac%7Bu%27%7D%7B2%5Csqrt%20u%7D)
5a(3a-2b):b(3a-2b)=5a:b=-2*5:-0,1=10:0,1=1 вроде так