| NR | Funkcja | Pochodna |
|---|---|---|
| 1. | \(\displaystyle f(x)=c \,\,\,\,\,\,c\in \mathbb{R} \) | \(\displaystyle f'(x)=0\) |
| 2. | \(\displaystyle f(x)=x^n \) | \(\displaystyle f'(x)=nx^{n-1} \) |
| 3. | \(\displaystyle f(x)=a^x\) | \(\displaystyle f'(x)=a^x\ln a\) |
| 4. | \(\displaystyle f(x)=e^x\) | \(\displaystyle f'(x)=e^x\) |
| 5. | \(\displaystyle f(x)=\ln x\) | \(\displaystyle f'(x)=\frac1x\) |
| 6. | \(\displaystyle f(x)=\log_a x\) | \(\displaystyle f'(x)=\frac{\log_a e }{x}\) |
| 7. | \(\displaystyle f(x)=\sin x\) | \(\displaystyle f'(x)=\cos x\) |
| 8. | \(\displaystyle f(x)=\cos x\) | \(\displaystyle f'(x)=-\sin x\) |
| 9. | \(\displaystyle f(x)=\text {tg}\, x\) | \(\displaystyle f'(x)=\frac1{\cos^2x}\) |
| 10. | \(\displaystyle f(x)=\text {ctg}\, x\) | \(\displaystyle f'(x)=-\frac1{\sin^2x}\) |
| 11. | \(\displaystyle f(x)=\arcsin x\) | \(\displaystyle f'(x)= \frac {1}{\sqrt{1-x^2}}\) |
| 12. | \(\displaystyle f(x)=\arccos x\) | \(\displaystyle f'(x)= \frac {-1}{\sqrt{1-x^2}}\) |
| 13. | \(\displaystyle f(x)=\text {arctg}\, x\) | \(\displaystyle f'(x)= \frac {1}{{1+x^2}}\) |
| 14. | \(\displaystyle f(x)=\text {arcctg}\, x\) | \(\displaystyle f'(x)= \frac {-1}{{1+x^2}}\) |
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