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What is the derivative of root 2x ?

User Ajameswolf
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1 Answer

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Answer:


\displaystyle (dy)/(dx) = (1)/(√(2x))

General Formulas and Concepts:

Calculus

Differentiation

  • Derivatives
  • Derivative Notation

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

Basic Power Rule:

  1. f(x) = cxⁿ
  2. f’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]:
\displaystyle (d)/(dx)[f(g(x))] =f'(g(x)) \cdot g'(x)

Explanation:

Step 1: Define

Identify


\displaystyle y = √(2x)

Step 2: Differentiate

  1. Basic Power Rule [Derivative Rule - Chain Rule]:
    \displaystyle y' = (1)/(2√(2x)) \cdot (d)/(dx)[2x]
  2. Basic Power Rule [Derivative Property - Multiplied Constant]:
    \displaystyle y' = (1)/(2√(2x)) \cdot 2
  3. Simplify:
    \displaystyle y' = (1)/(√(2x))

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

Unit: Differentiation

User Vasilii Muravev
by
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