The quotient of 2x-1 and 3x +5

1 answer:

5 0

"quotient of" means divide or fraction bar ... you should look for the word "and" to determine where to place your division sign or fraction bar
ANSWER:
$\frac{2x-1}{3x+5}$
or
(2x - 1) ÷ (3x + 5) ←Used parenthesis because they quantity 2x - 1 is separated from the quantity 3x + 5 by the word "and"

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Answer:

C. $\displaystyle \frac{cos(x)}{x} - ln(x)sin(x)$

General Formulas and Concepts:

Calculus

Differentiation

Derivatives
Derivative Notation

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

Trig Derivatives

Logarithmic Derivatives

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle f(x) = ln(x)cos(x)$

Step 2: Differentiate

Derivative Rule [Product Rule]: $\displaystyle f'(x) = \frac{d}{dx}[ln(x)]cos(x) + ln(x)\frac{d}{dx}[cos(x)]$
Logarithmic Derivative: $\displaystyle f'(x) = \frac{1}{x}cos(x) + ln(x)\frac{d}{dx}[cos(x)]$
Trig Derivative: $\displaystyle f'(x) = \frac{1}{x}cos(x) + ln(x)[-sin(x)]$
Simplify: $\displaystyle f'(x) = \frac{cos(x)}{x} - ln(x)sin(x)$