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

Ответ:

mgavyn1052

22.01.2022

Mathematics

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

General Formulas and Concepts:

Calculus

Differentiation

DerivativesDerivative 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:

f(x) = cxⁿf’(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

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

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

Unit: Differentiation

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