2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple

    Cards (70)

    • The Constant Rule states that if f(x) = c, where c is a constant, then f'(x) = 0
    • What is the derivative of the difference of two functions according to the Difference Rule?
      Difference of derivatives
    • What is the derivative of a constant multiple of a function according to the Constant Multiple Rule?
      Constant multiple of derivative
    • What is the formula for the Constant Multiple Rule?
      (kf(x))' = kf'(x)</latex>
    • What is the derivative of the sum of two functions according to the Sum Rule?
      Sum of derivatives
    • What is the derivative of the difference of two functions according to the Difference Rule?
      Difference of derivatives
    • If f(x) = x^3 and g(x) = 2x, what is (f - g)'(x) according to the Difference Rule?
      3x^2 - 2
    • The Difference Rule is similar to the Sum Rule, but uses subtraction instead of addition.

      True
    • The derivative of a constant is always zero.

      True
    • The Constant Rule states that the derivative of a constant is zero.
      True
    • The Difference Rule states that the derivative of the difference of two functions is the difference of their individual derivatives.

      True
    • If f(x) = 5x^2, what is (2f(x))'?
      20x
    • What is the derivative of any constant function according to the Constant Rule?
      Zero
    • What is the derivative of the sum of two functions according to the Sum Rule?
      Sum of derivatives
    • If f(x) = x^2 and g(x) = 3x, then (f + g)'(x) = 2x + 3 according to the Sum Rule.
      True
    • If f(x) = x^3 and g(x) = 2x, then (f - g)'(x) = 3x^2 - 2 according to the Difference Rule.

      True
    • If f(x) = 5, then f'(x) = 0 according to the Constant Rule.
      True
    • The Sum Rule states that if (f + g)'(x) = f'(x) + g'(x), then the operation being performed is sum
    • The Difference Rule states that if (f - g)'(x) = f'(x) - g'(x), then the operation being performed is difference
    • The Constant Multiple Rule states that if (kf(x))' = kf'(x), then the constant k is being multiplied by the derivative of f(x)
    • If f(x) = 2x^3, then f'(x) = 6x^2. Using the Constant Multiple Rule, we have (3f(x))' = 18x^2
    • The Sum Rule states that if (f + g)'(x) = f'(x) + g'(x), then the operation being performed is sum
    • The Difference Rule states that if (f - g)'(x) = f'(x) - g'(x), then the operation being performed is difference
    • What does the Difference Rule state for the derivative of (f - g)'(x)?
      f'(x) - g'(x)
    • What does the Constant Multiple Rule state for the derivative of (kf(x))'?
      kf'(x)
    • What is the derivative of f(x) = 5?
      0
    • What does the Sum Rule state for the derivative of (f + g)'(x)?
      f'(x) + g'(x)
    • What is (f - g)'(x) if f(x) = x^3 and g(x) = 2x?
      3x^2 - 2
    • What does the Constant Multiple Rule state about the derivative of a constant multiple of a function?
      Constant multiple of derivative
    • What does the Sum Rule state about the derivative of the sum of two functions?
      Sum of their derivatives
    • The derivative of a constant function is always zero
    • The Constant Rule applies when a function is constant and its derivative is 0.

      True
    • What is the formula for the Constant Multiple Rule?
      (kf(x))=(kf(x))' =kf(x) kf'(x)
    • Mathematically, the Constant Multiple Rule is (kf(x))' = kf'(x)
    • The Constant Multiple Rule contrasts with the Constant Rule, which results in a derivative of 0.

      True
    • If f(x)=f(x) =5 5, what is f(x)f'(x)?

      0
    • Mathematically, the Sum Rule is (f + g)'(x) = f'(x) + g'(x)
    • If f(x)=f(x) =x3 x^{3} and g(x)=g(x) =2x 2x, what is (f - g)'(x)</latex>?

      3x223x^{2} - 2
    • If f(x)=f(x) =2x3 2x^{3} and f(x)=f'(x) =6x2 6x^{2}, then (3f(x))=(3f(x))' =18x2 18x^{2} by applying the Constant Multiple Rule.18x^{2}
    • The derivative of a constant is always zero