8×1+5×(1/100)+9(1/1000)

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

2 years ago

Read 2 more answers

Write the following decimal number in its equivalent fraction form. Show all work for full credit.

Oduvanchick [21]

Negative 3143 over 1000 divide -3.143 by 1000 and there’s your answer

4 0

2 years ago

I’m stuck on number 8 plz help anyone !!

levacccp [35]

Answer:

Sally's km/h during the first half hour is 7 .

The lowest average speed is between the 3rd and 4th stops.

Step-by-step explanation:

On the table during the first half hour, Sally traveled 7 km.

From the first stop to the second stop, she traveled 8 km; from the second stop to the third stop, she traveled 6 km; from the third stop to the fourth stop, she traveled 3 km; from the fourth stop to the fifth stop, she traveled 4 km; and from the fifth stop to the sixth stop she traveled 8 km. Therefore The lowest average speed is between the 3rd and 4th stops.

Plz rate Brainliest because this took a long time.

8 0

3 years ago

1 Solve: -8–2k=-2(k+4)

Olegator [25]

Answer:

zero=0

Explanation:

-8-2k=-2(k+4)

-8-2k=-2k-8

-2k+2k=-8+8

zero=0

4 0

2 years ago

Frank's age is one fourth of Danas age what equation can represent this

Katen [24]

Take x as Danas age,
equation,

x×1/4= x

hope this helps....

7 0

3 years ago