Trigonometric derivative rules

Trigonometric functions derivatives:

• `d/{dx} sin(x) = cos(x)`
• `d/{dx} cos(x) = - sin(x)`
• `d/{dx} tan(x) = sec^2(x)`
• `d/{dx} cot(x) = - csc^2(x)`
• `d/{dx} sec(x) = sec(x) tan(x)`
• `d/{dx} csc(x) = - csc(x) cot(x)`

Inverse trigonometric functions derivatives:

• `d/{dx} arcsin(x) = 1/{1 - x^2}`
• `d/{dx} arccos(x) = -1/ { √(1 - x^2) } `
• `d/{dx} arctan(x) = 1/ { 1 + x^2 } `
• `d/{dx} arccot(x) = -1/ { 1 + x^2 } `
• `d/{dx} arcsec(x) = 1/ { |x| √(x^2 - 1) } `
• `d/{dx} arccsc(x) = -1/ { |x| √(x^2 - 1 } `

Hyperbolic functions derivatives:

• `d/{dx} sinh(x) = cosh(x)`
• `d/{dx} cosh(x) = sinh(x)`
• `d/{dx} tanh(x) = sech^2(x)`
• `d/{dx} coth(x) = -csch^2(x)`
• `d/{dx} sech(x) = -sech(x) tanh(x)`
• `d/{dx} csc(x) = -csch(x) coth(x)`