Question

Find the derivative of
y= 1/(3x^3)

Answer 1

`\displaystyle y' = (-1)/(x^4)`

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)/(3x^3)`

Step 2: Differentiate

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

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

Unit: Differentiation