Will the difference between 44,041 and 43,876 be greater or less than, 1,000 explain

1 answer:

4 0

Answer:

Less

Step-by-step explanation:

44,041 - 43,876 is 165 and that is less than 1,000.

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Step2247 [10]

Answer:

$\displaystyle y' = \frac{y - 5x}{x + 6y^2}$

General Formulas and Concepts:

Algebra I

Calculus

Differentiation

Derivative Property [Multiplied Constant]: $\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)$

Derivative Property [Addition/Subtraction]: $\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]$

Basic Power Rule:

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

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

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle 5x^2 - 2xy + 4y^3 = 5$

Step 2: Differentiate

Implicit Differentiation: $\displaystyle \frac{dy}{dx}[5x^2 - 2xy + 4y^3] = \frac{dy}{dx}[5]$
Rewrite [Derivative Property - Addition/Subtraction]: $\displaystyle \frac{dy}{dx}[5x^2] - \frac{dy}{dx}[2xy] + \frac{dy}{dx}[4y^3] = \frac{dy}{dx}[5]$
Rewrite [Derivative Property - Multiplied Constant]: $\displaystyle 5\frac{dy}{dx}[x^2] - 2\frac{dy}{dx}[xy] + 4\frac{dy}{dx}[y^3] = \frac{dy}{dx}[5]$
Basic Power Rule [Chain Rule]: $\displaystyle 10x - 2\frac{dy}{dx}[xy] + 12y^2y' = 0$
Product Rule: $\displaystyle 10x - 2\bigg[ \frac{dy}{dx}[x]y + x\frac{dy}{dx}[y] \bigg] + 12y^2y' = 0$
Basic Power Rule [Chain Rule]: $\displaystyle 10x - 2\bigg[ y + xy' \bigg] + 12y^2y' = 0$
Simplify: $\displaystyle 10x - 2y + 2xy' + 12y^2y' = 0$
Isolate y' terms: $\displaystyle 2xy' + 12y^2y' = 2y - 10x$
Factor: $\displaystyle y'(2x + 12y^2) = 2y - 10x$
Isolate y': $\displaystyle y' = \frac{2y - 10x}{2x + 12y^2}$
Factor: $\displaystyle y' = \frac{2(y - 5x)}{2(x + 6y^2)}$
Simplify: $\displaystyle y' = \frac{y - 5x}{x + 6y^2}$