1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ExtremeBDS [4]
3 years ago
11

Find the derivative of

\sqrt[3]{x} " alt=" y = \sqrt[3]{x} " align="absmiddle" class="latex-formula">
at the point where x = 27.​
Mathematics
1 answer:
MAXImum [283]3 years ago
8 0

Answer:

\displaystyle y'(27) = \frac{1}{27}

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right<u> </u>

<u>Algebra I</u>

  • Exponential Rule [Root Rewrite]: \displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}
  • Exponential Rule [Rewrite]: \displaystyle b^{-m} = \frac{1}{b^m}

<u>Calculus</u>

Derivatives

Derivative Notation

Basic Power Rule

  • f(x) = cxⁿ
  • f’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

<u>Step 1: Define</u>

y = ∛x

x = 27

<u>Step 2: Differentiate</u>

  1. [Function] Rewrite [Exponential Rule - Root Rewrite]:                               \displaystyle y = x^{\frac{1}{3}}
  2. Basic Power Rule:                                                                                         \displaystyle y' = \frac{1}{3}x^{\frac{1}{3} - 1}
  3. Simplify:                                                                                                         \displaystyle y' = \frac{1}{3}x^{-\frac{2}{3}}
  4. Rewrite [Exponential Rule - Rewrite]:                                                           \displaystyle y' = \frac{1}{3x^{\frac{2}{3}}}

<u>Step 3: Solve</u>

  1. Substitute<em> </em>in <em>x</em> [Derivative]:                                                                           \displaystyle y'(27) = \frac{1}{3(27)^{\frac{2}{3}}}
  2. Evaluate exponents:                                                                                     \displaystyle y'(27) = \frac{1}{3(9)}
  3. Multiply:                                                                                                         \displaystyle y'(27) = \frac{1}{27}

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

Unit: Derivatives

Book: College Calculus 10e

You might be interested in
Please help!!
zalisa [80]
The answer to your question is 0.667
4 0
3 years ago
The inequality 2x - 3y ≥ 5 is satisfied by point (1/2, 1/3).<br> True<br> False
Blizzard [7]
The correct answer for this statement would be FALSE. Let us try to prove it by plugging in the values. So 2 (1/2) - 3 (1/3) <span> ≥ 5.
So that would be 1 - 3 </span><span> ≥ 5..
-2 </span><span> ≥ 5, which makes the result false because -2 is not more than or equal to 5, but instead, it is less than. I hope this answer helps. </span>
4 0
3 years ago
Read 2 more answers
Select all the expressions that are equivalent to -90x+60.
Ber [7]

Answer:A, B and C

Step-by-step explanation:

7 0
3 years ago
I need help for number 19, please
wlad13 [49]

Answer:

\large\boxed{x=-3i}

Step-by-step explanation:

(x-i)^5=32(x+i)^5\\\\(x-i)^5=2^5(x+i)^5\qquad\text{use}\ (ab)^n=a^nb^n\\\\(x-i)^5=\bigg(2(x+i)\bigg)^5\iff x-i=2(x+i)\qquad\text{use distributive property}\\\\x-i=2x+2i\qquad\text{add}\ i\ \text{to both sides}\\\\x=2x+3i\qquad\text{subtract 2x from both sides}\\\\-x=3i\qquad\text{chnage the signs}\\\\x=-3i

5 0
3 years ago
2.<br> Which arc is a major arc?<br> POR<br> PSQ<br> PQ<br> SO
Ann [662]

Answer:

your right

Step-by-step explanation:

4 0
3 years ago
Other questions:
  • Here you guys go. Please help more on these probs.
    9·1 answer
  • Divide and write in simplest form 2 3/4 divided by 2 1/5
    13·1 answer
  • (4,-10); m=-3 I need help in this problem
    5·1 answer
  • In the notation below, X is the random variable, c is a constant, and V refers to the variance.
    15·1 answer
  • 19/10 as in simplest
    13·2 answers
  • Does anybody know the answer to all of these?
    13·2 answers
  • Is "A quotient of a number and seven" a expression or equation
    5·1 answer
  • Do you agree that the government should help people who are jobless or homeless? If so, how do you think they should help? For h
    12·1 answer
  • Three figures exist such that abcd ≅ ghij and bcda ≅ rstu. if gh = 6 cm, hi = 8 cm, ij = 10 cm, and gj = 9 cm, what is ts? 6 cm
    7·1 answer
  • (
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!