Inverse trigonometric functions/Derivative/Fact

The inverse trigonometric functions have the following derivatives.

1. ${}{\left(\arcsin x\right)}'={\frac {1}{\sqrt {1-x^{2}}}}\,.$

2. ${}{\left(\arccos x\right)}'=-{\frac {1}{\sqrt {1-x^{2}}}}\,.$

3. ${}{\left(\arctan x\right)}'={\frac {1}{1+x^{2}}}\,.$

4. ${}{\left(\operatorname {arccot} x\right)}'=-{\frac {1}{1+x^{2}}}\,.$

Proof, Write another proof