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Product and Quotient Rules quiz

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  • What is the correct way to find the derivative of two functions being added together?
    Take the derivatives of each function separately and add them together.
  • Why can't you simply multiply the derivatives of two functions to find the derivative of their product?
    Because the derivative of a product is not equal to the product of the derivatives; you must use the product rule.
  • State the product rule for the derivative of two functions f(x) and g(x).
    The product rule is f(x) * g'(x) + g(x) * f'(x).
  • What mnemonic can help you remember the product rule?
    The mnemonic is 'left d right plus right d left.'
  • When applying the product rule to h(x) = (x - 5)(2x + 9), what is h'(x)?
    h'(x) = 4x - 1.
  • In the product rule, what does 'd' stand for in the mnemonic?
    'd' stands for taking the derivative.
  • What is the derivative of y = (2x² - 1)(3 + x³) using the product rule?
    y' = 10x⁴ - 3x² + 12x.
  • What is the first step when applying the product rule to two multiplied functions?
    Multiply the first function by the derivative of the second, then add the second function times the derivative of the first.
  • What rule must you use to find the derivative of two functions being divided?
    You must use the quotient rule.
  • State the quotient rule for the derivative of f(x)/g(x).
    The quotient rule is [g(x) * f'(x) - f(x) * g'(x)] / [g(x)]².
  • What mnemonic can help you remember the quotient rule?
    The mnemonic is 'low d high minus high d low over the square of what's below.'
  • When applying the quotient rule to h(x) = x / (3x - 4), what is h'(x)?
    h'(x) = -4 / (3x - 4)².
  • In the quotient rule mnemonic, what do 'high' and 'low' refer to?
    'High' refers to the numerator function and 'low' refers to the denominator function.
  • What is the derivative of y = (2x² - 1)/(3 - x³) using the quotient rule?
    y' = [-2x⁴ - 3x² + 12x] / (3 - x³)².
  • When using the quotient rule, what should you do with the denominator after applying the rule?
    You can usually leave the denominator as is, squared, unless simplification is obvious.