Pochodne funkcji elementarnych

1. (c)^′ =  0

2. (xⁿ)^′ =  nx^n − 1

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

4. (sinx)^′ =  cosx

5. (cosx)^′ =   − sinx

6. $\left( \operatorname{tg}x \right)^{'} = \ \frac{1}{\operatorname{}x}$

7. $\left( \operatorname{ctg}x \right)^{'} = \ \frac{- 1}{\operatorname{}x}$

8. (a^x)^′ =  a^xlna

9. (e^x)^′ =  e^x

10. $\left( \operatorname{}x \right)^{'} = \ \frac{1}{x\ln a}$

11. $\left( \ln x \right)^{'} = \ \frac{1}{x}$

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

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

14. $\left( \operatorname{arctg}x \right)^{'} = \ \frac{1}{1 + x^{2}}$

15. $\left( \operatorname{arcctg}x \right)^{'} = \ \frac{- 1}{1 + x^{2}}$

16. (sinhx)^′ =  coshx

17. (coshx)^′ =  sinhx

18. $\left( \operatorname{tgh}x \right)^{'} = \ \frac{1}{\operatorname{}x}$

19. $\left( \operatorname{ctgh}x \right)^{'} = \ \frac{- 1}{\operatorname{}x}$

20. $\left( \operatorname{arcsinh}x \right)^{'} = \ \frac{1}{\sqrt{x^{2} + 1}}$

21. $\left( \operatorname{arccosh}x \right)^{'} = \ \frac{1}{\sqrt{x^{2} - 1}}$

22. $\left( \operatorname{arctgh}x \right)^{'} = \ \frac{1}{1 - x^{2}}$

23. $\left( \operatorname{arcctgh}x \right)^{'} = \ \frac{- 1}{1 - x^{2}}$