Question

find the derivative u(x)=4\3x-1

Answer 1

Answer:

$\displaystyle u'(x) = \frac{-12}{(3x - 1)^2}$

General Formulas and Concepts:

Calculus

Differentiation

• Derivatives
• Derivative Notation

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

Derivative Property [Addition/Subtraction]:                                                        $\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]$  

Basic Power Rule:

1. f(x) = cxⁿ
2. f’(x) = c·nxⁿ⁻¹

Derivative Rule [Quotient Rule]:                                                                           $\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}$

Derivative Rule [Chain Rule]:                                                                                 $\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle u(x) = \frac{4}{3x - 1}$

Step 2: Differentiate

1. Derivative Rule [Quotient Rule]:                                                                   $\displaystyle u'(x) = \frac{(4)'(3x - 1) - 4(3x - 1)'}{(3x - 1)^2}$
2. Basic Power Rule [Derivative Properties]:                                                   $\displaystyle u'(x) = \frac{-4(3)}{(3x - 1)^2}$
3. Simplify:                                                                                                         $\displaystyle u'(x) = \frac{-12}{(3x - 1)^2}$

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

Unit: Differentiation