派生数学函数

下列是由固有数学函数派生的非固有数学函数：

函数派生的等效公式Secant（正割）Sec(X) = 1 / Cos(X)Cosecant（余割）Cosec(X) = 1 / Sin(X)Cotangent（余切）Cotan(X) = 1 / Tan(X)Inverse Sine（反正弦）Arcsin(X) = Atn(X / Sqr(-X * X + 1))Inverse Cosine（反余弦）Arccos(X) = Atn(-X / Sqr(-X * X + 1)) + 2 * Atn(1)Inverse Secant（反正割）Arcsec(X) = Atn(X / Sqr(X * X - 1)) + Sgn((X) -1) * (2 * Atn(1))Inverse Cosecant（反余割）Arccosec(X) = Atn(X / Sqr(X * X - 1)) + (Sgn(X) - 1) * (2 * Atn(1))Inverse Cotangent（反余切）Arccotan(X) = Atn(X) + 2 * Atn(1)Hyperbolic Sine（双曲正弦）HSin(X) = (Exp(X) - Exp(-X)) / 2 Hyperbolic Cosine（双曲余弦）HCos(X) = (Exp(X) + Exp(-X)) / 2Hyperbolic Tangent（双曲正切）HTan(X) = (Exp(X) - Exp(-X)) / (Exp(X) + Exp(-X))Hyperbolic Secant（双曲正割）HSec(X) = 2 / (Exp(X) + Exp(-X))Hyperbolic Cosecant（双曲余割）HCosec(X) = 2 / (Exp(X) - Exp(-X))Hyperbolic Cotangent（双曲余切）HCotan(X) = (Exp(X) + Exp(-X)) / (Exp(X) - Exp(-X))Inverse Hyperbolic Sine（反双曲正弦）HArcsin(X) = Log(X + Sqr(X * X + 1))Inverse Hyperbolic Cosine（反双曲余弦）HArccos(X) = Log(X + Sqr(X * X - 1))Inverse Hyperbolic Tangent（反双曲正切）HArctan(X) = Log((1 + X) / (1 - X)) / 2Inverse Hyperbolic Secant（反双曲正割）HArcsec(X) = Log((Sqr(-X * X + 1) + 1) / X)Inverse Hyperbolic Cosecant（反双曲余割）HArccosec(X) = Log((Sgn(X) * Sqr(X * X + 1) +1) / X)Inverse Hyperbolic Cotangent（反双曲余切）HArccotan(X) = Log((X + 1) / (X - 1)) / 2以 N 为底的对数LogN(X) = Log(X) / Log(N)