Question

What’s the derivative of y = 1/(2x^5)?

Answer 1

`\displaystyle y' = (-5)/(2x^6)`

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

Explanation:

Step 1: Define

Identify

`\displaystyle y = (1)/(2x^5)`

Step 2: Differentiate

1. Rewrite:
   `\displaystyle y = (x^(-5))/(2)`
2. Derivative Property [Multiplied Constant]:
   `\displaystyle y' = (1)/(2) (d)/(dx)[x^(-5)]`
3. Basic Power Rule:
   `\displaystyle y' = (1)/(2)(-5x^(-6))`
4. Simplify:
   `\displaystyle y' = (-5)/(2x^6)`

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

Unit: Differentiation