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Lana71 [14]
3 years ago
6

Please help with this AP Calculus question !

Mathematics
1 answer:
melomori [17]3 years ago
7 0

Answer:

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

General Formulas and Concepts:

<u>Calculus</u>

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:

<u>Step 1: Define</u>

<em>Identify</em>

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

<u>Step 2: Differentiate</u>

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

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

Unit: Differentiation

Book: College Calculus 10e

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