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
9
Zarrin [17]

Answer:

oa

Step-by-step explanation:

7 0
3 years ago
Identify the reflection of the figure with vertices E(8,4), F(-16,-8), and G(24,-16) across the y-axis.
Dafna1 [17]

Answer:

\boxed{\text{E$'$(-8, 4), F$'$(16,-8), G$'$(-24,-16)}}

Step-by-step explanation:

When you reflect a point (x, y) in the y-axis, the y-coordinate remains the same, but the x-coordinate gets the opposite sign. Thus,

E (8,4) ⟶ E' (-8,4)

F (-16,-8) ⟶ F' (16,-8)

G (24,-16) ⟶ G' (-24,-16)

\text{The reflected figure has coordinates } \boxed{\textbf{E$'$(-8, 4), F$'$(16,-8), G$'$(-24,-16)}}

The figure EFG and its reflection E'F'G' are shown in the diagram below.

6 0
3 years ago
X + 20 is greater than 4x -1
Paul [167]

Answer:

False; they are equal.

Step-by-step explanation:

The equation is x + 20 > 4x - 1.

First, do the opposite of -1 and add one to the other side while -1+1 cancels out. Now it's x+21 > 4x. Now subtract x from both sides. Positive x minus negative x cancels out and 4x minus x or 1x is 3x. Now you're left with 21> 3x. Now do the inverse operation of multiplication and divide both sides by 3. Now the 3x over 3 cancels out and 21 divided by 3 is 7. So x is 7. If you substitute it in. It will be 7+20 which is 27 which is great than 4(7)-1 which is 28-1. 28-1 is 27. So, the equation is false. They are equal.

7 0
3 years ago
Suppose $1,000 is borrowed for one year at 8% simple interest. How much is due at the end of the year to
AleksAgata [21]

Answer:

you will be bankrupt simple!

6 0
3 years ago
Read 2 more answers
Help pls i will give brainliest answer
natita [175]

Examine one full set:

12/8

simplify

3/2

filling in

3  2

9  6

12  8

18  12

7 0
3 years ago
Other questions:
  • The circle is inscribed in triangle A E C. Which are congruent line segments? Select two options. AB and CB ;EF and ED; ED and C
    13·2 answers
  • Is ( -1 , 2 ) the solution to the system involving y=-1x+1and y=3x+5?
    6·1 answer
  • Please answer quickly! I’m so confused and I have no idea what to do! I will mark brainliest!
    9·2 answers
  • The school store sells pencils for $0.30 each,hats for $14.50 each,and binders for $3.20 each.Elena would like to buy 3 pencils,
    15·2 answers
  • Find the distance from E to F
    14·1 answer
  • What is the slope of the line that passes through the points (-2, 7) and (2, -5)?
    6·1 answer
  • Use the web to find a data file containing information of your interest (i.e. energy consumption, financialtime series, biomedic
    7·1 answer
  • If we have a square with an area of 75 square meters, what would the side length be?
    12·2 answers
  • Write the algebraic expression for ‘x plus five is twenty three’
    5·1 answer
  • A slice was made through the shape shown below. The slice is parallel to the base of the shape. What is the shape of the cross s
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!