Mathematics, 07.11.2020 05:40 unknowntay04

Find derivative for 3x³ + 2xy + 4y²=0.

Answers: 2

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Answers

Answer from: ht2005

$y'=\frac{-9x^2-2y}{2(x+4y)}$

General Formulas and Concepts:

Algebra

Equality Properties

Calculus

Chain Rule: $\frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$ Basic Power Rule: f’(x) = c·nxⁿ⁻¹Derivative of a constant equals 0Implicit Differentiation

Step-by-step explanation:

Step 1: Define equation

3x³ + 2xy + 4y² = 0

Step 2: Find 1st Derivative

Set up Derivative: $\frac{dy}{dx} [3x^3 + 2xy + 4y^2 = 0]$ Take Implicit Differentiation: 9x^2+(2y+2xy')+8yy'=0

Step 3: Find Derivative (Solve for y')

Define:

Move 9x² over: 2y+2xy'+8yy'=-9x^2

Move 2y over: 2xy'+8yy'=-9x^2-2y

Factor y': y'(2x+8y)=-9x^2-2y

Isolate y': $y'=\frac{-9x^2-2y}{2x+8y}$ Factor GCF: $y'=\frac{-9x^2-2y}{2(x+4y)}$

Answer from: Keemdadream13

$\frac{dy}{dx}= -\frac{9x^2+2y}{2(x+4y)}$

Step-by-step explanation:

Find the derivative of 3x^3 + 2xy + 4y^2 = 0 .

In order to find the derivative of this function, $\frac{dy}{dx}$ , we can start by noticing that there are two variables in this problem, x and y.

Since we want the derivative with respect to x, every time we encounter the variable “y” in this problem we can change it to $\frac{dy}{dx}$ . We will see this happen later on in the solving process by using implicit differentiation.

Let’s start by taking the derivative of the entire function:

$\frac{d}{dx} (3x^3 + 2xy + 4y^2 = 0)$

Using the Power Rule and the Product Rule, we can perform implicit differentiation on this equation. Let’s take the derivative of each separate piece in this function:

$3x^3 \rightarrow 3(3x^3^-^1) \rightarrow 9x^2$ Power Rule

$2xy \rightarrow (2x \times \frac{dy}{dx} + y \times 2)$ Product Rule

$4y^2 \rightarrow 2(4y) \times \frac{dy}{dx} \rightarrow 8y \times \frac{dy}{dx}$ Power Rule & Implicit Differentiation

Let’s combine these steps into one comprehensive operation:

$9x^2 + (2x \times \frac{dy}{dx} + y \times 2) + 8y \times \frac{dy}{dx} = 0$

Simplify.

$9x^2 + 2x\frac{dy}{dx} + 2y + 8y \frac{dy}{dx} = 0$

Keep all terms containing $\frac{dy}{dx}$ on the left side of the equation and move everything else to the right side of the equation. This way we can solve for $\frac{dy}{dx}$ , which, in this case, is the derivative of the original function.

Subtract 9x^2 and from both sides of the equation.

$2x\frac{dy}{dx} +8y \frac{dy}{dx} = -9x^2-2y$

Factor out dy/dx from the left side of the equation.

$\frac{dy}{dx}(2x+8y) = -9x^2-2y$

Divide both sides of the equation by (2x + 8y).

$\frac{dy}{dx}= \frac{-9x^2-2y}{2x+8y}$

You can leave it in this form, or you can convert this to either:

$\frac{dy}{dx}= \frac{-9x^2-2y}{2(x+4y)}$ $\frac{dy}{dx}= -\frac{9x^2+2y}{2(x+4y)}$

Answer from: Quest

function 2 has a greater rate of change than function 1

function 2 has a greater y-intercept than function 1

step-by-step explanation:

$\newline{\text{the rate of change is change per unit time}}$ $\newline{\text{for (x,y), rate of change is }\frac{y_2-y_1}{x_2-x_1} \text{ or change in y divided by change in x}}$ $\newline{\text{for function 1, the cost goes up by 75-45=30 each time every hour}}$ $\newline{\text{that means that the slope of function 1 is 30 per hour}}$ $\newline{\text{for the 2nd function, 40 is added every hour. therefor, the slope is 40 per hour}}$ $\bigskip\newline{\text{since 40 per hour> 30 per hour, function 2 has a greater rate of change than function 1}}$ $\bigskip\newline{\text{the y intercept is the y value when x is 0}}$ $\newline{\text{for function 1, the y value when x is 0 is 45}}$ $\newline{\text{for function 2, the y value when x is 0 (or the flat rate) is 50}}$ $\newline{\text{since 50> 45, function 2 has a greater y intercept than funciton 1}}$ $\bigskip\bigskip\newline{\text{the answers are: }}$ $\newline{\text{ function 2 has a greater rate of change than function 1}}$ $\newline{\text{function 2 has a greater y-intercept than function 1.}}$

Answer from: Quest

i can not answer the question due to the fact that you spelled "carton" as "cartoon", a cartoon is something you watch on tv, a carton is a box that holds things. and also you've been waiting for this question for a while so why don't you get off your lazy a** and try to figure it out for yourself for once!

step-by-step explanation:

===============================================================^

look above, and leave your comments down below, and don't for get a five stars and a and brainliest xd

sorry for the stars in the middle of words its because it wouldn't let me submit. xd

How many cartoon of food an how many cartoons of clothing should be sent with each plane? including

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