Calcora

• diff_constant — Constant → 0 e.g. 5, pi, e
• diff_identity — Identity → 1 e.g. x
• sum_rule — Sum: (f+g)' = f' + g' e.g. x + sin(x)
• constant_multiple — Constant multiple: (c·f)' = c·f' e.g. 3*x**2
• power_rule — Power: (x^n)' = n·x^(n-1) e.g. x**5
• product_rule — Product: (f·g)' = f'·g + f·g' e.g. x*sin(x)
• quotient_rule — Quotient: (f/g)' = (f'·g - f·g')/g² e.g. sin(x)/x
• logarithmic_differentiation — (u^v)' with both varying e.g. x**x

• chain_rule_sin — sin(u)' = cos(u)·u' e.g. sin(x**2)
• chain_rule_cos — cos(u)' = -sin(u)·u' e.g. cos(3*x)
• chain_rule_tan — tan(u)' = sec²(u)·u' e.g. tan(x**2)
• chain_rule_sec — sec(u)' = sec(u)tan(u)·u' e.g. sec(x)
• chain_rule_csc — csc(u)' = -csc(u)cot(u)·u' e.g. csc(x)
• chain_rule_cot — cot(u)' = -csc²(u)·u' e.g. cot(x)

• chain_rule_asin — asin(u)' = u'/√(1-u²) e.g. asin(x)
• chain_rule_acos — acos(u)' = -u'/√(1-u²) e.g. acos(x)
• chain_rule_atan — atan(u)' = u'/(1+u²) e.g. atan(x)
• chain_rule_asec — asec(u)' with chain rule e.g. asec(x)
• chain_rule_acsc — acsc(u)' with chain rule e.g. acsc(x)
• chain_rule_acot — acot(u)' with chain rule e.g. acot(x)

• chain_rule_sinh — sinh(u)' = cosh(u)·u' e.g. sinh(x**2)
• chain_rule_cosh — cosh(u)' = sinh(u)·u' e.g. cosh(x)
• chain_rule_tanh — tanh(u)' = sech²(u)·u' e.g. tanh(x)
• chain_rule_asinh — asinh(u)' with chain rule e.g. asinh(x)
• chain_rule_acosh — acosh(u)' with chain rule e.g. acosh(x)
• chain_rule_atanh — atanh(u)' with chain rule e.g. atanh(x)

• chain_rule_exp — exp(u)' = exp(u)·u' e.g. exp(x**2)
• chain_rule_log — log(u)' = u'/u e.g. log(x)

• chain_rule_erf — erf(u)' = (2/√π)·exp(-u²)·u' e.g. erf(x**2)
• chain_rule_gamma — gamma(u)' = Γ(u)·ψ(u)·u' e.g. gamma(x)
• chain_rule_heaviside — Heaviside(u)' = δ(u)·u' e.g. Heaviside(x)
• chain_rule_abs — |u|' = sign(u)·u' e.g. Abs(x**3)
• chain_rule_floor — ⌊u⌋' = 0 (except at integers) e.g. floor(x)
• chain_rule_ceiling — ⌈u⌉' = 0 (except at integers) e.g. ceiling(x)

• matrix_multiply — Multiply two matrices element-by-element A × B
• matrix_determinant — Calculate determinant (2×2, 3×3, n×n) det(A)
• matrix_inverse — Find inverse matrix A⁻¹ A⁻¹ where AA⁻¹ = I
• matrix_rref — Row reduce to echelon form RREF(A)
• matrix_eigenvalues — Find eigenvalues and eigenvectors Av = λv
• matrix_lu — LU decomposition with pivoting PA = LU

💡 Symbolic Matrices: Use quoted strings for symbols: [["a","b"],["c","d"]]
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