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IgorLugansk [536]
4 years ago
15

How do i find the derivative of

9 \div \sqrt{x} " alt="9 \div \sqrt{x} " align="absmiddle" class="latex-formula">
Mathematics
1 answer:
Alekssandra [29.7K]4 years ago
4 0
Possible derivation:
d/dx(3)
The derivative of 3 is zero:
Answer: = 0
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See explanation.

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
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<u>Algebra I</u>

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<u>Calculus</u>

Limits

  • Right-Side Limit:                                                                                             \displaystyle  \lim_{x \to c^+} f(x)
  • Left-Side Limit:                                                                                               \displaystyle  \lim_{x \to c^-} f(x)

Limit Rule [Variable Direct Substitution]:                                                             \displaystyle \lim_{x \to c} x = c

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

\displaystyle f(x) = \left \{ {{\sqrt{x + 1}, \ x < 3} \atop {5 - x, \ x \geq 3}} \right.

<u>Step 2: Find Right Limit</u>

  1. Substitute in variables [Right-Side Limit]:                                                      \displaystyle  \lim_{x \to 3^+} 5 - x
  2. Evaluate limit [Limit Rule - Variable Direct Substitution]:                           \displaystyle  \lim_{x \to 3^+} 5 - x = 5 - 3
  3. Subtract:                                                                                                         \displaystyle  \lim_{x \to 3^+} 5 - x = 2

∴ the right-side limit equals 2.

<u>Step 3: Find Left Limit</u>

  1. Substitute in variables [Left-Side Limit]:                                                       \displaystyle  \lim_{x \to 3^-} \sqrt{x + 1}
  2. Evaluate limit [Limit Rule - Variable Direct Substitution]:                           \displaystyle  \lim_{x \to 3^-} \sqrt{x + 1} = \sqrt{3 + 1}
  3. [√Radical] Add:                                                                                             \displaystyle  \lim_{x \to 3^-} \sqrt{x + 1} = \sqrt{4}
  4. [√Radical] Evaluate:                                                                                       \displaystyle  \lim_{x \to 3^-} \sqrt{x + 1} = 2

∴ the left-side limit equals 2.

<u>Step 4: Find Limit</u>

<em>The right and left-side limits are equal.</em>

∴  \displaystyle  \lim_{x \to 3} f(x) = 2

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

Unit: Limits

Book: College Calculus 10e

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