Gr12 Mathematics: Ch 5.3 Rules for Differentiation
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Questions and Answers

What is the derivative of x^n with respect to x?

  • nx^n
  • x^(n+1)
  • nx^(n-1) (correct)
  • (n-1)x^n

    • What is the derivative of a constant k with respect to x?

  • kx
  • 0 (correct)
  • -k
  • 1

    • What is the derivative of k*f(x) with respect to x?

  • k*x*f(x)
  • k*f'(x) (correct)
  • f(x)*kx
  • f(x)/k

    • What is the derivative of f(x) + g(x) with respect to x?

    <p>f'(x) + g'(x)</p> Signup and view all the answers

    What is the derivative of f(x) - g(x) with respect to x?

    <p>f'(x) - g'(x)</p> Signup and view all the answers

    When should you use the first principles method for differentiation?

    <p>When the question specifically requests to use first principles or when asked to differentiate using the definition of a derivative</p> Signup and view all the answers

    What is the notation for the derivative of y = f(x) with respect to x?

    <p>All of the above</p> Signup and view all the answers

    What are the symbols D and d/dx called in differentiation?

    <p>Differential operators</p> Signup and view all the answers

    What is the general rule for differentiating x raised to the power of a real number?

    <p>d/dx[x^n] = nx^(n-1)</p> Signup and view all the answers

    What is the derivative of a constant multiple of a function?

    <p>k * d/dx[f(x)]</p> Signup and view all the answers

    Which of the following is a correct notation for the derivative of y with respect to x?

    <p>dy/dx</p> Signup and view all the answers

    When should you use the rules for differentiation?

    <p>When the question does not specify how to determine the derivative</p> Signup and view all the answers

    What is the derivative of the sum of two functions?

    <p>d/dx[f(x)] + d/dx[g(x)]</p> Signup and view all the answers

    What is the purpose of the differential operators D and d/dx?

    <p>To indicate the operation of differentiation</p> Signup and view all the answers

    What is the derivative of a function minus another function?

    <p>d/dx[f(x)] - d/dx[g(x)]</p> Signup and view all the answers

    Why do we use the rules for differentiation?

    <p>To simplify the process of finding derivatives</p> Signup and view all the answers

    What is the derivative of the function f(x) = 2x^3 with respect to x?

    <p>6x^2</p> Signup and view all the answers

    If g(x) is a function, what is the derivative of f(x) = 3g(x) with respect to x?

    <p>3g'(x)</p> Signup and view all the answers

    What is the derivative of the function f(x) = x^2 + 2x with respect to x?

    <p>2x + 2</p> Signup and view all the answers

    What is the notation for the derivative of the function y = f(x) with respect to x, where y is the dependent variable and x is the independent variable?

    <p>dy/dx</p> Signup and view all the answers

    What is the derivative of the function f(x) = x^4 - 2x^2 with respect to x?

    <p>4x^3 - 4x</p> Signup and view all the answers

    What is the purpose of the differential operators D and d/dx in differentiation?

    <p>To indicate the operation of differentiation</p> Signup and view all the answers

    What is the derivative of the function f(x) = 2x^2 + 3x with respect to x?

    <p>4x + 3</p> Signup and view all the answers

    If f(x) and g(x) are functions, what is the derivative of f(x) = 2f(x) + 3g(x) with respect to x?

    <p>2f'(x) + 3g'(x)</p> Signup and view all the answers

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