Таблица производных сложных функций

1. \((y^n)' = n y^{n-1} \cdot y'\)
2. \((\sqrt{y})' = \dfrac{1}{2\sqrt{y}} \cdot y'\)
3. \((e^y)' = e^y \cdot y'\)
4. \((a^y)' = a^y \ln a \cdot y'\)
5. \((\sin y)' = \cos y \cdot y'\)
6. \((\cos y)' = -\sin y \cdot y'\)
7. \((\operatorname{tg} y)' = \dfrac{1}{\cos^2 y} \cdot y'\)
8. \((\operatorname{ctg} y)' = -\dfrac{1}{\sin^2 y} \cdot y'\)
9. \((\ln y)' = \dfrac{1}{y} \cdot y'\)
10. \((\log_a y)' = \dfrac{1}{y \ln a} \cdot y'\)
11. \((\arcsin y)' = \dfrac{1}{\sqrt{1 - y^2}} \cdot y'\)
12. \((\arccos y)' = -\dfrac{1}{\sqrt{1 - y^2}} \cdot y'\)
13. \((\operatorname{arctg} y)' = \dfrac{1}{1 + y^2} \cdot y'\)
14. \((\operatorname{arcctg} y)' = -\dfrac{1}{1 + y^2} \cdot y'\)