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Differentiation formulas (Assume $f (x)$ and $g (x)$ exist, $a$ and $c$ are constants)			Integration formulas
1. $y = c\cdot x^n \rightarrow \frac{dy}{dx} = c\cdot nx^{n-1}$	2. $y = f(x)\cdot g(x) \rightarrow \frac{dy}{dx} = f(x)\cdot g'(x)+g(x)\cdot f'(x)$		20. $\int u^n \, du = \frac{u^{n+1}}{n+1}+c~(\mbox{if}~n \ne 1)$	21. $\int \frac{du}{u} = \ln \|u\|+c$
3. $y = \frac{f(x)}{g(x)} \rightarrow \frac{dy}{dx} = \frac{g(x)\cdot f'(x)-f(x)\cdot g'(x)}{[g(x)]^2}$	4. $y = [f(x)]^n \rightarrow \frac{dy}{dx} = n\cdot [f(x)]^{n-1}\cdot f'(x)$		22. $\int \sin u\, du = -\cos u + c$	23. $\int \cos u\, du = \sin u + c$
5. $y = \sin f(x) \rightarrow \frac{dy}{dx} = [\cos f(x)]\cdot f'(x)$	6. $y = \cos f(x) \rightarrow \frac{dy}{dx} = [-\sin f(x)]\cdot f'(x)$		24. $\int \tan u\, du = -\ln \|\cos u\| + c$	25. $\int \cot u\, du = \ln \|\sin u\| + c$
7. $y = \tan f(x) \rightarrow \frac{dy}{dx} = [\sec^2 f(x)]\cdot f'(x)$	8. $y = \cot f(x) \rightarrow \frac{dy}{dx} = [-\csc^2 f(x)]\cdot f'(x)$		26. $\int \sec^2 u\, du = \tan u + c$	27. $\int \csc^2 u\, du = -\cot u + c$
9. $y = \sec f(x) \rightarrow \frac{dy}{dx} = [\sec f(x)\cdot \tan f(x)]\cdot f'(x)$	10. $y = \csc f(x) \rightarrow \frac{dy}{dx} = [-\csc f(x)\cdot \cot f(x)]\cdot f'(x)$		28. $\int \sec u\cdot \tan u\, du = \sec u + c$	29. $\int \csc u\cdot \cot u\, du = -\csc u + c$
11. $y = \ln f(x) \rightarrow \frac{dy}{dx} = \frac{f'(x)}{f(x)}$	12. $y = \log_a f(x) \rightarrow \frac{dy}{dx} = \frac{f'(x)}{f(x)\cdot \ln a}$		30. $\int \sec u\, du = \ln \|\sec u + \tan u\| + c$	31. $\int \csc u\, du = -\ln \|\csc u + \cot u\| + c$
13. $y = e^{f(x)} \rightarrow \frac{dy}{dx} = e^{f(x)}\cdot f'(x)$	14. $y = \sin^{-1} f(x) \rightarrow \frac{dy}{dx} = \frac{f'(x)}{\sqrt{1-[f(x)]^2}}$		32. $\int e^u\, du = e^u + c$	33. $\int a^u\, du = \frac{a^u}{\ln a} + c$
15. $y = \cos^{-1} f(x) \rightarrow \frac{dy}{dx} = \frac{-f'(x)}{\sqrt{1-[f(x)]^2}}$	16. $y = \tan^{-1} f(x) \rightarrow \frac{dy}{dx} = \frac{f'(x)}{1+[f(x)]^2}$		34. $\int \frac{du}{\sqrt{a^2-u^2}} = \sin^{-1} \frac{u}{a} + c~(\mbox{if}~a > 0)$	35. $\int \frac{du}{a^2-u^2} = \frac{1}{a}\tan^{-1} \frac{u}{a} + c~(\mbox{if}~a \ne 0)$
17. $y = \cot^{-1} f(x) \rightarrow \frac{dy}{dx} = \frac{-f'(x)}{1+[f(x)]^2}$	18. $y = \sec^{-1} f(x) \rightarrow \frac{dy}{dx} = \frac{f'(x)}{f(x)\cdot \sqrt{[f(x)]^2-1}}$		36. $\int \frac{du}{u\sqrt{u^2-a^2}} = \frac{1}{a}\sec^{-1} \frac{u}{a} + c~(\mbox{if}~a > 0)$
19. $y = \csc^{-1} f(x) \rightarrow \frac{dy}{dx} = \frac{-f'(x)}{f(x)\cdot \sqrt{[f(x)]^2-1}}$			37. Integration by Parts $\int u\,dv = uv - \int v\,du$

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