В треугольнике ABC AC=BC, угол С равен 50 градусов. найдите внешний угол CBD
1 ответ:
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А) 
(производная произведения)
![y' = 3,5*[(x^4)' * e^{2x} + (x^4) * (e^{2x})' ] = \\ \\ = 3,5*(4x^3 *e^{2x} + x^4 * 2e^{2x}) = 7x^3 e^{2x} (2+x)](https://tex.z-dn.net/?f=y%27+%3D+3%2C5%2A%5B%28x%5E4%29%27+%2A+e%5E%7B2x%7D+%2B+%28x%5E4%29+%2A+%28e%5E%7B2x%7D%29%27+%5D+%3D++%5C%5C++%5C%5C+%3D+3%2C5%2A%284x%5E3+%2Ae%5E%7B2x%7D+%2B+x%5E4+%2A+2e%5E%7B2x%7D%29+%3D+7x%5E3+e%5E%7B2x%7D+%282%2Bx%29)
б)
(производная частного)
в)![y = x^3 * \sqrt[3]{x^2} * \sqrt[6]{x}](https://tex.z-dn.net/?f=y+%3D+x%5E3+%2A++%5Csqrt%5B3%5D%7Bx%5E2%7D+%2A++%5Csqrt%5B6%5D%7Bx%7D+)
(производная степенной функции)
![y' = (x^3 * \sqrt[3]{x^2} * \sqrt[6]{x} )' = (x^3 * x^{ \frac{2}{3} } * x^{ \frac{1}{6} })' = (x^{ \frac{23}{6} })' = \frac{23}{6} x^{ \frac{17}{6} }](https://tex.z-dn.net/?f=y%27+%3D+%28x%5E3+%2A++%5Csqrt%5B3%5D%7Bx%5E2%7D+%2A++%5Csqrt%5B6%5D%7Bx%7D+%29%27+%3D+%28x%5E3+%2A+x%5E%7B+%5Cfrac%7B2%7D%7B3%7D+%7D+%2A+x%5E%7B+%5Cfrac%7B1%7D%7B6%7D+%7D%29%27+%3D+%28x%5E%7B+%5Cfrac%7B23%7D%7B6%7D+%7D%29%27+%3D++%5Cfrac%7B23%7D%7B6%7D+x%5E%7B+%5Cfrac%7B17%7D%7B6%7D+%7D)
г)![y = \sqrt[4]{x^7+lnx}](https://tex.z-dn.net/?f=y+%3D++%5Csqrt%5B4%5D%7Bx%5E7%2Blnx%7D++)
(производная сложной функции)
![y' = (\sqrt[4]{x^7+lnx} )' = ((x^7+lnx ) ^{ \frac{1}{4} })' = \\ \\ = \frac{1}{4} (x^7+lnx ) ^{ -\frac{3}{4} } * (x^7+lnx)' = \\ \\ = \frac{1}{4\sqrt[4]{(x^7+lnx)^3} } *(7x^6+ \frac{1}{x} )](https://tex.z-dn.net/?f=y%27+%3D++%28%5Csqrt%5B4%5D%7Bx%5E7%2Blnx%7D+%29%27+%3D+%28%28x%5E7%2Blnx+%29+%5E%7B+%5Cfrac%7B1%7D%7B4%7D+%7D%29%27+%3D++%5C%5C++%5C%5C+%3D++%5Cfrac%7B1%7D%7B4%7D+%28x%5E7%2Blnx+%29+%5E%7B+-%5Cfrac%7B3%7D%7B4%7D+%7D+%2A+%28x%5E7%2Blnx%29%27+%3D++%5C%5C++%5C%5C+%3D+%5Cfrac%7B1%7D%7B4%5Csqrt%5B4%5D%7B%28x%5E7%2Blnx%29%5E3%7D+%7D+%2A%287x%5E6%2B++%5Cfrac%7B1%7D%7Bx%7D+%29)
б)
в)
г)