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![y=5cos6x \
y'=5*(-sin6x)*6=-30sin6x](https://tex.z-dn.net/?f=y%3D5cos6x+%5C+%0Ay%27%3D5%2A%28-sin6x%29%2A6%3D-30sin6x "y=5cos6x \
y'=5*(-sin6x)*6=-30sin6x")
3.
![y=x^3e^x \
y'=3x^2e^x+x^3e^x](https://tex.z-dn.net/?f=y%3Dx%5E3e%5Ex+%5C+%0Ay%27%3D3x%5E2e%5Ex%2Bx%5E3e%5Ex "y=x^3e^x \
y'=3x^2e^x+x^3e^x")
4.
![y=7sin(5x- pi ) \
y'=7cos(5x- pi )*5=35cos(5x- pi )](https://tex.z-dn.net/?f=y%3D7sin%285x-+pi+%29+%5C+%0Ay%27%3D7cos%285x-+pi+%29%2A5%3D35cos%285x-+pi+%29 "y=7sin(5x- pi ) \
y'=7cos(5x- pi )*5=35cos(5x- pi )")
5.
![y=x^2tgx \
y'=2xtgx+ frac{x^2}{cos^2x}= frac{2xsinx}{cosx}+ frac{x^2}{cos^2x}= frac{2xsinxcosx+x^2}{cos^2x}= \ \
= frac{xsin2x+x^2}{cos^2x}](https://tex.z-dn.net/?f=y%3Dx%5E2tgx+%5C+%0Ay%27%3D2xtgx%2B+frac%7Bx%5E2%7D%7Bcos%5E2x%7D%3D+frac%7B2xsinx%7D%7Bcosx%7D%2B+frac%7Bx%5E2%7D%7Bcos%5E2x%7D%3D+frac%7B2xsinxcosx%2Bx%5E2%7D%7Bcos%5E2x%7D%3D+%5C++%5C+%0A%3D+frac%7Bxsin2x%2Bx%5E2%7D%7Bcos%5E2x%7D+++++ "y=x^2tgx \
y'=2xtgx+ frac{x^2}{cos^2x}= frac{2xsinx}{cosx}+ frac{x^2}{cos^2x}= frac{2xsinxcosx+x^2}{cos^2x}= \ \
= frac{xsin2x+x^2}{cos^2x}")
6.
![y=3e^{4x+1} \
y'=3e^{4x+1}*4=12e^{4x+1}](https://tex.z-dn.net/?f=y%3D3e%5E%7B4x%2B1%7D+%5C+%0Ay%27%3D3e%5E%7B4x%2B1%7D%2A4%3D12e%5E%7B4x%2B1%7D "y=3e^{4x+1} \
y'=3e^{4x+1}*4=12e^{4x+1}")
7.
![y=e^xlnx \
y'=e^xlnx+ frac{e^x}{x}](https://tex.z-dn.net/?f=y%3De%5Exlnx+%5C+%0Ay%27%3De%5Exlnx%2B+frac%7Be%5Ex%7D%7Bx%7D+ "y=e^xlnx \
y'=e^xlnx+ frac{e^x}{x}")
8.
![y=lncosx \
y'= frac{1}{cosx}*(-sinx)=-tgx](https://tex.z-dn.net/?f=y%3Dlncosx+%5C+%0Ay%27%3D+frac%7B1%7D%7Bcosx%7D%2A%28-sinx%29%3D-tgx+ "y=lncosx \
y'= frac{1}{cosx}*(-sinx)=-tgx")
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