Question

Find the derivative of 2x+x^2/x

Answer 1

`\displaystyle (dy)/(dx) = 1`

General Formulas and Concepts:

Calculus

Differentiation

• Derivatives
• Derivative Notation

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:

Step 1: Define

Identify

`\displaystyle y = (2x + x^2)/(x)`

Step 2: Differentiate

1. Factor:
   `\displaystyle y = (x(2 + x))/(x)`
2. Simplify:
   `\displaystyle y = 2 + x`
3. Derivative Property [Addition/Subtraction]:
   `\displaystyle y' = (d)/(dx)[2] + (d)/(dx)[x]`
4. Basic Power Rule:
   `\displaystyle y' = 1`

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

Unit: Differentiation