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What is the derivative of 4x+ k​

1 Answer

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Answer:


\displaystyle (dy)/(dx) = 4

General Formulas and Concepts:

Calculus

Differentiation

  • Derivatives
  • Derivative Notation

Derivative Property [Multiplied Constant]:
\displaystyle (d)/(dx) [cf(x)] = c \cdot f'(x)

Derivative Property [Addition/Subtraction]:
\displaystyle (d)/(dx)[f(x) + g(x)] = (d)/(dx)[f(x)] + (d)/(dx)[g(x)]

Basic Power Rule:

  1. f(x) = cxⁿ
  2. f’(x) = c·nxⁿ⁻¹

Explanation:

*Note:

Treat k as an arbitrary constant.

Step 1: Define

Identify


\displaystyle y = 4x + k

Step 2: Differentiate

  1. Derivative Property [Addition/Subtraction]:
    \displaystyle y' = (d)/(dx)[4x] + (d)/(dx)[k]
  2. Rewrite [Derivative Property - Multiplied Constant]:
    \displaystyle y' = 4 (d)/(dx)[x] + (d)/(dx)[k]
  3. Basic Power Rule:
    \displaystyle y' = 4

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

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