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Derivatives of Inverse Trigonometric Functions quiz #1

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Termini in questo insieme (10)

  • What is the derivative of the inverse sine function, arcsin(x), and what is the domain restriction for x?
    The derivative of arcsin(x) is 1 divided by the square root of (1 minus x squared), or d/dx[arcsin(x)] = 1 / √(1 - x²), with the restriction that |x| < 1.
  • How do you find the derivative of the inverse cosine function, arccos(x), and what is the domain restriction for x?
    The derivative of arccos(x) is negative one divided by the square root of (1 minus x squared), or d/dx[arccos(x)] = -1 / √(1 - x²), with the restriction that |x| < 1.
  • What is the derivative of the inverse tangent function, arctan(x)?
    The derivative of arctan(x) is 1 divided by (1 plus x squared), or d/dx[arctan(x)] = 1 / (1 + x²).
  • State the derivative of the inverse cotangent function, arccot(x).
    The derivative of arccot(x) is negative one divided by (1 plus x squared), or d/dx[arccot(x)] = -1 / (1 + x²).
  • What is the derivative of the inverse secant function, arcsec(x), and what is the domain restriction for x?
    The derivative of arcsec(x) is 1 divided by the absolute value of x times the square root of (x squared minus 1), or d/dx[arcsec(x)] = 1 / (|x|√(x² - 1)), with the restriction that |x| > 1.
  • How do you find the derivative of the inverse cosecant function, arccsc(x), and what is the domain restriction for x?
    The derivative of arccsc(x) is negative one divided by the absolute value of x times the square root of (x squared minus 1), or d/dx[arccsc(x)] = -1 / (|x|√(x² - 1)), with the restriction that |x| > 1.
  • When differentiating a function involving an inverse trigonometric function with a more complex argument, such as arcsin(3x + 2), what rule must be applied?
    You must use the chain rule: differentiate the outer inverse trig function as usual, then multiply by the derivative of the inner function.
  • What is the derivative of the inverse sine function, arcsin(x), and what is the domain restriction for x?
    The derivative of arcsin(x) is 1 divided by the square root of (1 minus x squared), or d/dx[arcsin(x)] = 1 / √(1 - x²), with the restriction that |x| < 1.
  • How do you find the derivative of the inverse cosine function, arccos(x), and what is the domain restriction for x?
    The derivative of arccos(x) is negative one divided by the square root of (1 minus x squared), or d/dx[arccos(x)] = -1 / √(1 - x²), with the restriction that |x| < 1.
  • When differentiating a function involving an inverse trigonometric function with a more complex argument, such as arcsin(3x + 2), what rule must be applied?
    You must use the chain rule: differentiate the outer inverse trig function as usual, then multiply by the derivative of the inner function.