Triangle ABC is transformed to triangle A′B′C′, as shown below:

Implicit differentiation Please help

Anvisha [2.4K]

Answer:

$y''(-1) =8$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Algebra I

Factoring

Calculus

Implicit Differentiation

The derivative of a constant is equal to 0

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Product Rule: $\frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)$

Chain Rule: $\frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Quotient Rule: $\frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}$

Step-by-step explanation:

Step 1: Define

-xy - 2y = -4

Rate of change of the tangent line at point (-1, 4)

Step 2: Differentiate Pt. 1

Find 1st Derivative

Implicit Differentiation [Product Rule/Basic Power Rule]: $-y - xy' - 2y' = 0$
[Algebra] Isolate y' terms: $-xy' - 2y' = y$
[Algebra] Factor y': $y'(-x - 2) = y$
[Algebra] Isolate y': $y' = \frac{y}{-x-2}$
[Algebra] Rewrite: $y' = \frac{-y}{x+2}$

Step 3: Find y

Define equation: $-xy - 2y = -4$
Factor y: $y(-x - 2) = -4$
Isolate y: $y = \frac{-4}{-x-2}$
Simplify: $y = \frac{4}{x+2}$

Step 4: Rewrite 1st Derivative

[Algebra] Substitute in y: $y' = \frac{-\frac{4}{x+2} }{x+2}$
[Algebra] Simplify: $y' = \frac{-4}{(x+2)^2}$

Step 5: Differentiate Pt. 2

Find 2nd Derivative

Differentiate [Quotient Rule/Basic Power Rule]: $y'' = \frac{0(x+2)^2 - 8 \cdot 2(x + 2) \cdot 1}{[(x + 2)^2]^2}$
[Derivative] Simplify: $y'' = \frac{8}{(x+2)^3}$

Step 6: Find Slope at Given Point

[Algebra] Substitute in x: $y''(-1) = \frac{8}{(-1+2)^3}$
[Algebra] Evaluate: $y''(-1) =8$

6 0

3 years ago

Read 2 more answers

0.38, 1.52)

Elis [28]

Answer:

The best correct option is C

x = 1.79 to x = 3

Step-by-step explanation:

Making the sport off all little thing that crowed. They are still grouped into 7. Option C is theost appropriate.

5 0

2 years ago

Complete two expressions that have the same product as 3 x 5. 12

likoan [24]

The two expressions that would have the same product as 3.5 x 5.12 are:

184.32 x 1/12

76.8 x 3/12

<h3>What is the product of the a number?</h3>

The product of a number is the value that is derived when two or more numbers are multiplied by each other.

Product of 3 and 5.12 is 15.36.

In order to determine what number should be multipled by 1/12 to yield 15.36, multiply 15.36 by 12: 15.36 x 12 = 184.32

In order to determine what number should be multipled by 3/12 to yield 15.36, multiply 15.36 by 4: 15.36 x 4 = 76.8

To learn more about multiplication, please check: brainly.com/question/13814687

4 0

1 year ago

Type the correct answer in each box.

vesna_86 [32]

Answer:

X=60°

Y=50°

Step-by-step explanation:

Triangles must equal 180° when you add all angles together.

Triangle with angle X

50+70=120
180-120=60
X=60°

To find the value of Y takes a few more steps, but it isn't hard!

Angle Y is on a line, which equals 180° just like a triangle.

We know X=60°, but we don't know what the blank angle equals.

We use the same steps as we did when finding X

60+50=110
180-110=70
Blank angle=70°

We know that the blank angle=70° and that X=60°

Since the line equals 180, we add the two angles and then subtract from 180, just like before!

70+60=130
180-130=50
Y=50°

5 0

2 years ago

What is 12/14 in its simplest form

Fofino [41]

Answer:

its about 0.8571

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers