Question

Derivative of square root 24x

Answer 1

`\displaystyle (d)/(dx) = (√(6x))/(x)`

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 = √(24x)`

Step 2: Differentiate

1. Basic Power Rule [Derivative Rule - Chain Rule]:
   `\displaystyle y' = (1)/(2√(24x)) \cdot (d)/(dx)[24x]`
2. Basic Power Rule [Derivative Property - Multiplied Constant]:
   `\displaystyle y' = (24)/(2√(24x))`
3. Simplify:
   `\displaystyle y' = (12)/(√(24x))`
4. Rationalize:
   `\displaystyle y' = (12√(24x))/(24x)`
5. Simplify:
   `\displaystyle y' = (√(6x))/(x)`

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

Unit: Differentiation