# Derivative of trigonometric functions

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##### Examples
###### Lessons
1. $\frac{{d}}{{{d}x}}\;\sin \left( {\;\;\;\;} \right) = \cos \left( {\;\;\;\;} \right) \cdot \frac{{d}}{{{d}x}}\left( {\;\;\;\;} \right)$
$\frac{{d}}{{{d}x}}\;\cos \left( {\;\;\;\;} \right) = - \sin \left( {\;\;\;\;} \right) \cdot \frac{{d}}{{{d}x}}\left( {\;\;\;\;} \right)$
$\frac{{d}}{{{d}x}}\;\tan \left( {\;\;\;\;} \right) = {\sec ^2}\left( {\;\;\;\;} \right) \cdot \frac{{d}}{{{d}x}}\left( {\;\;\;\;} \right)$
$\frac{{d}}{{{d}x}}{\;cot}\left( {\;\;\;\;} \right) = - {\csc ^2}\left( {\;\;\;\;} \right) \cdot \frac{{d}}{{{d}x}}\left( {\;\;\;\;} \right)$
$\frac{{d}}{{{d}x}}\;\sec \left( {\;\;\;\;} \right) = \sec \left( {\;\;\;\;} \right)\tan \left( {\;\;\;\;} \right) \cdot \frac{{d}}{{{d}x}}\left( {\;\;\;\;} \right)$
$\frac{{d}}{{{d}x}}\;\csc \left( {\;\;\;\;} \right) = - \csc \left( {\;\;\;\;} \right)\cot \left( {\;\;\;\;} \right) \cdot \frac{{d}}{{{d}x}}\left( {\;\;\;\;} \right)$
1. Differentiate:
a) $y = {\sin ^4}x$
b) $y = sin\left( {{x^4}} \right)$
1. $\frac{{d}}{{{d}x}}\;\sin (\cos (\tan x))$