Derivative of trigonometric functions

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  1. ddxโ€…โ€Šsinโก(โ€…โ€Šโ€…โ€Šโ€…โ€Šโ€…โ€Š)=cosโก(โ€…โ€Šโ€…โ€Šโ€…โ€Šโ€…โ€Š)โ‹…ddx(โ€…โ€Šโ€…โ€Šโ€…โ€Šโ€…โ€Š)\frac{{d}}{{{d}x}}\;\sin \left( {\;\;\;\;} \right) = \cos \left( {\;\;\;\;} \right) \cdot \frac{{d}}{{{d}x}}\left( {\;\;\;\;} \right)
    ddxโ€…โ€Šcosโก(โ€…โ€Šโ€…โ€Šโ€…โ€Šโ€…โ€Š)=โˆ’sinโก(โ€…โ€Šโ€…โ€Šโ€…โ€Šโ€…โ€Š)โ‹…ddx(โ€…โ€Šโ€…โ€Šโ€…โ€Šโ€…โ€Š)\frac{{d}}{{{d}x}}\;\cos \left( {\;\;\;\;} \right) = - \sin \left( {\;\;\;\;} \right) \cdot \frac{{d}}{{{d}x}}\left( {\;\;\;\;} \right)
    ddxโ€…โ€Štanโก(โ€…โ€Šโ€…โ€Šโ€…โ€Šโ€…โ€Š)=secโก2(โ€…โ€Šโ€…โ€Šโ€…โ€Šโ€…โ€Š)โ‹…ddx(โ€…โ€Šโ€…โ€Šโ€…โ€Šโ€…โ€Š)\frac{{d}}{{{d}x}}\;\tan \left( {\;\;\;\;} \right) = {\sec ^2}\left( {\;\;\;\;} \right) \cdot \frac{{d}}{{{d}x}}\left( {\;\;\;\;} \right)
    ddxโ€…โ€Šcot(โ€…โ€Šโ€…โ€Šโ€…โ€Šโ€…โ€Š)=โˆ’cscโก2(โ€…โ€Šโ€…โ€Šโ€…โ€Šโ€…โ€Š)โ‹…ddx(โ€…โ€Šโ€…โ€Šโ€…โ€Šโ€…โ€Š)\frac{{d}}{{{d}x}}{\;cot}\left( {\;\;\;\;} \right) = - {\csc ^2}\left( {\;\;\;\;} \right) \cdot \frac{{d}}{{{d}x}}\left( {\;\;\;\;} \right)
    ddxโ€…โ€Šsecโก(โ€…โ€Šโ€…โ€Šโ€…โ€Šโ€…โ€Š)=secโก(โ€…โ€Šโ€…โ€Šโ€…โ€Šโ€…โ€Š)tanโก(โ€…โ€Šโ€…โ€Šโ€…โ€Šโ€…โ€Š)โ‹…ddx(โ€…โ€Šโ€…โ€Šโ€…โ€Šโ€…โ€Š)\frac{{d}}{{{d}x}}\;\sec \left( {\;\;\;\;} \right) = \sec \left( {\;\;\;\;} \right)\tan \left( {\;\;\;\;} \right) \cdot \frac{{d}}{{{d}x}}\left( {\;\;\;\;} \right)
    ddxโ€…โ€Šcscโก(โ€…โ€Šโ€…โ€Šโ€…โ€Šโ€…โ€Š)=โˆ’cscโก(โ€…โ€Šโ€…โ€Šโ€…โ€Šโ€…โ€Š)cotโก(โ€…โ€Šโ€…โ€Šโ€…โ€Šโ€…โ€Š)โ‹…ddx(โ€…โ€Šโ€…โ€Šโ€…โ€Šโ€…โ€Š)\frac{{d}}{{{d}x}}\;\csc \left( {\;\;\;\;} \right) = - \csc \left( {\;\;\;\;} \right)\cot \left( {\;\;\;\;} \right) \cdot \frac{{d}}{{{d}x}}\left( {\;\;\;\;} \right)
    1. Differentiate:
      a) y=sinโก4xy = {\sin ^4}x
      b) y=sin(x4)y = sin\left( {{x^4}} \right)
      1. ddxโ€…โ€Šsinโก(cosโก(tanโกx))\frac{{d}}{{{d}x}}\;\sin (\cos (\tan x))