Derivação de funções trigonométricas

Sendo $u(x)$ uma função derivável temos que:

$$(\sin u{)}^{\prime }=(\cos u)\cdot u^{\prime }$$ $$(\cos u{)}^{\prime }=-(\sin u)\cdot u^{\prime }$$ $$(\tan u{)}^{\prime }=({\sec }^{2}u)\cdot u^{\prime }$$ $$(\cot u{)}^{\prime }=-({\csc }^{2}u)\cdot u^{\prime }$$ $$(\sec u{)}^{\prime }=(\sec u\cdot \tan u)\cdot u^{\prime }$$ $$(\csc u{)}^{\prime }=-(\csc u\cdot \cot u)\cdot u^{\prime }$$ $$(\arcsin u{)}^{\prime }=\frac{u^{\prime }}{\sqrt{1-u^2}}$$ $$(\arccos u{)}^{\prime }=-\frac{u^{\prime }}{\sqrt{1-u^2}}$$ $$(\arctan u{)}^{\prime }=\frac{u^{\prime }}{1+u^2}$$