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Derivatives of Inverse Trigonometric Functions definitions

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  • Inverse Sine
    A function whose derivative is 1 divided by the square root of 1 minus the input squared, with input restricted between -1 and 1.
  • Inverse Cosine
    A function whose derivative is negative 1 over the square root of 1 minus the input squared, with input restricted between -1 and 1.
  • Inverse Tangent
    A function whose derivative is 1 divided by 1 plus the input squared, defined for all real numbers.
  • Inverse Cotangent
    A function whose derivative is negative 1 over 1 plus the input squared, defined for all real numbers.
  • Inverse Secant
    A function whose derivative is 1 over the absolute value of the input times the square root of the input squared minus 1, with input greater than 1 or less than -1.
  • Inverse Cosecant
    A function whose derivative is negative 1 over the absolute value of the input times the square root of the input squared minus 1, with input greater than 1 or less than -1.
  • Implicit Differentiation
    A technique for finding derivatives when a function is defined implicitly, often used for inverse trigonometric functions.
  • Chain Rule
    A method for differentiating composite functions by multiplying the derivative of the outer function by the derivative of the inner function.
  • Product Rule
    A rule for differentiating products of two functions, involving the sum of each function times the derivative of the other.
  • Domain Restriction
    A limitation on input values, such as requiring the input to be between -1 and 1 for certain inverse trigonometric derivatives.
  • Square Root Expression
    An expression involving the square root, commonly appearing in denominators of inverse trigonometric derivatives.
  • Absolute Value
    A function that returns the non-negative value of its input, often used in denominators for inverse secant and cosecant derivatives.
  • Power Rule
    A rule for differentiating expressions raised to a power, involving multiplying by the exponent and reducing the power by one.
  • Trig Identity
    An equation involving trigonometric functions, such as sine squared plus cosine squared equals one, used to simplify derivatives.