# Formula Sheet Library
## MTH Student Academy

### Calculus I & II
| Topic | Formula |
|-------|---------|
| Power Rule | d/dx [x^n] = nx^(n-1) |
| Product Rule | d/dx [uv] = u'v + uv' |
| Quotient Rule | d/dx [u/v] = (u'v - uv') / v^2 |
| Chain Rule | d/dx [f(g(x))] = f'(g(x)) * g'(x) |
| Fundamental Theorem | ∫[a,b] f(x) dx = F(b) - F(a) |

### Linear Algebra
| Concept | Definition/Formula |
|---------|--------------------|
| Matrix Multi. | (AB)_ij = Σ k=1 to n A_ik * B_kj |
| Determinant (2x2) | det(A) = ad - bc |
| Eigenvalue Eq. | det(A - λI) = 0 |
| Vector Dot Product | a · b = Σ a_i * b_i |

### Probability & Statistics
| Metric | Formula |
|--------|---------|
| Expected Value | E[X] = Σ x * P(X=x) |
| Variance | Var(X) = E[X^2] - (E[X])^2 |
| Bayes' Rule | P(A\|B) = [P(B\|A) * P(A)] / P(B) |
| Normal Dist. | Z = (X - μ) / σ |