গণিতের ফর্মূলা

 গণিতের ফর্মূলাঃ

1. $$ (a+b)^2=a^2+2ab+b^2$$

2. $$ (a-b)^2=a^2-2ab+b^2$$

ব্যবকলনঃ

1.$$\frac{d}{dx} (c) = 0 \quad \text{(Constant Rule)} \\$$
2.$$\frac{d}{dx} (x^n) = n x^{n-1} \quad \text{(Power Rule)} \\$$
3.$$\frac{d}{dx} (e^x) = e^x \quad \text{(Exponential Function)} \\$$
4.$$\frac{d}{dx} (\ln x) = \frac{1}{x} \quad \text{(Logarithm Rule)} \\$$
5.$$\frac{d}{dx} (\sin x) = \cos x \\$$
6.$$\frac{d}{dx} (\cos x) = -\sin x \\$$
7.$$\frac{d}{dx} (\tan x) = \sec^2 x \\$$
8.$$\frac{d}{dx} (\cot x) = -\csc^2 x \\$$
9.$$\frac{d}{dx} (\sec x) = \sec x \tan x \\$$
10.$$\frac{d}{dx} (\csc x) = -\csc x \cot x \\$$
11.$$\frac{d}{dx} (uv) = u'v + uv' \quad \text{(Product Rule)} \\$$
12.$$\frac{d}{dx} \left( \frac{u}{v} \right) = \frac{u' v - u v'}{v^2} \quad \text{(Quotient Rule)} \\$$

সমাকলনঃ

1. $$\int c \, dx = cx + C \quad \text{(Constant Rule)} \\$$

2. $$\int x^n \, dx = \frac{x^{n+1}}{n+1} + C, \quad n \neq -1 \\$$

3. $$\int e^x \, dx = e^x + C \\$$

4. $$\int \frac{1}{x} \, dx = \ln |x| + C \\$$

5. $$\int \sin x \, dx = -\cos x + C \\$$

6. $$\int \cos x \, dx = \sin x + C \\$$

7. $$\int \sec^2 x \, dx = \tan x + C \\$$

8. $$\int \csc^2 x \, dx = -\cot x + C \\$$

9. $$\int \sec x \tan x \, dx = \sec x + C \\$$

10. $$\int \csc x \cot x \, dx = -\csc x + C \\$$

11. $$\int \frac{1}{x^2 + a^2} \, dx = \frac{1}{a} \tan^{-1} \frac{x}{a} + C \\$$

12. $$\int \frac{1}{\sqrt{a^2 - x^2}} \, dx = \sin^{-1} \frac{x}{a} + C \\$$

13. $$\int \frac{1}{a^2 + x^2} \, dx = \frac{1}{a} \tan^{-1} \frac{x}{a} + C \\$$

14. $$\int \frac{1}{\sqrt{x^2 - a^2}} \, dx = \ln |x + \sqrt{x^2 - a^2}| + C\\$$