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
vaieri [72.5K]
3 years ago
12

Find the derivative of

Mathematics
1 answer:
kirill [66]3 years ago
6 0

Answer:

\displaystyle y'(1, \frac{3}{2}) = -3

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>

  • Coordinates (x, y)
  • Functions
  • Function Notation
  • Terms/Coefficients
  • 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>

<u />\displaystyle y = \frac{3}{2x^2}<u />

\displaystyle \text{Point} \ (1, \frac{3}{2})

<u>Step 2: Differentiate</u>

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

<u>Step 3: Solve</u>

  1. Substitute in coordinate [Derivative]:                                                              \displaystyle y'(1, \frac{3}{2}) = \frac{-3}{1^3}
  2. Evaluate exponents:                                                                                         \displaystyle y'(1, \frac{3}{2}) = \frac{-3}{1}
  3. Divide:                                                                                                               \displaystyle y'(1, \frac{3}{2}) = -3

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

Unit: Derivatives

Book: College Calculus 10e

You might be interested in
If Shelly wants to earn the most interest on her account, but knows she can only keep $100 in her account, which bank's checking
rjkz [21]

Answer:

Chases bank account?

Step-by-step explanation:

3 0
4 years ago
Awser to this questin
kobusy [5.1K]


180 times 4/100= 7.20- Sales tax

180+7.20= $187.20 is the total cost
Please mark brainliest and give a thanks...

5 0
4 years ago
Read 2 more answers
An investor makes an investment of $1,000,000.00 to buy a small, select service hotel in Daytona Beach. She achieves a
baherus [9]

Answer:

In terms of %, it's 20%.

Step-by-step explanation:

Used an ROI calculator:

7 0
3 years ago
Picture attached please help!
Aleonysh [2.5K]
The answer is 12.56.

I just used the area of circle formula

The formula is 3.14 x r^2

2 x 2 is 4

4 x 3.14 is 12.56


Pls mark brainleist
3 0
3 years ago
Adrianna spent $131 on clothes. Pants, (p), cost $28 and shirts, (s), cost $15. If she bought a total of 7 items, how many shirt
saveliy_v [14]

the correct answer is a) 5

8 0
3 years ago
Other questions:
  • 40% of what number is 10.2?
    13·1 answer
  • Find the value of z.
    8·1 answer
  • Name two quadrilaterals in which all the sides have an equal length
    8·2 answers
  • A pair of jeans is on sale for 25% off the original price. Which expression represents the sale price? If the original price is
    6·1 answer
  • How do I mark brainliest
    13·2 answers
  • Write a multiplication equation using one whole number and one fraction that have a product of 18/8.
    14·1 answer
  • Which of the following is a secant?
    8·1 answer
  • Find the distance between the points (-3,-6) and (3,2)
    11·2 answers
  • To make 5 blueberry pies, Mindy needs about 2 pounds of blueberries. How many pounds of blueberries does Mindy need to make 20 b
    5·2 answers
  • What is the answer can someone explain it
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!