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Basic Rules of Differentiation quiz

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  • What is the derivative of any constant function?
    The derivative of any constant function is always 0.
  • What is the derivative of the function f(x) = x?
    The derivative of f(x) = x is always 1.
  • State the sum and difference rule for derivatives.
    The derivative of a sum or difference is the sum or difference of the derivatives.
  • How does the constant multiple rule work when differentiating?
    You can pull the constant out front and multiply it by the derivative of the function.
  • What does the power rule state for differentiating x^n?
    The derivative of x^n is n times x to the (n-1) power.
  • Can the power rule be used for negative exponents?
    Yes, the power rule works for any real exponent, including negative exponents.
  • How do you rewrite 1/x to use the power rule for differentiation?
    Rewrite 1/x as x^(-1) before applying the power rule.
  • What is the derivative of x^6 using the power rule?
    The derivative is 6x^5.
  • How do you differentiate f(x) = x^4 + x^3?
    Differentiate each term separately to get 4x^3 + 3x^2.
  • What is the derivative of g(x) = 3x^2?
    The derivative is 6x.
  • What is the derivative of x^(-3)?
    The derivative is -3x^(-4), or equivalently, -3/x^4.
  • How do you find the derivative of x^(3/2)?
    The derivative is (3/2)x^(1/2).
  • What is the derivative of f(x) = 1/x?
    The derivative is -1/x^2.
  • How do you differentiate the cube root of x?
    Rewrite as x^(1/3) and the derivative is (1/3)x^(-2/3).
  • Why is the derivative of a constant function always zero?
    Because the slope of the tangent line to a constant function is always zero.