x^(3)+2y^(2)-xy=2 Find the value of (dy)/(dx) at the point (0,-1). Choose 1 answer: (A) 4 (B) -(1)/(4) (C) (1)/(4) (D) -4

Differentiate Implicitly: Implicitly differentiate both sides of the equation with respect to x. (d)/(dx)(x^(3)+2y^(2)-xy) = (d)/(dx)(2)Differentiate Terms: Differentiate each term separately. (d)/(dx)(x^(3)) = 3x^(2), (d)/(dx)(2y^(2)) = 4y(dy)/(dx), (d)/(dx)(-xy) = -y - x(dy)/(dx), (d)/(dx)(2) = 0Combine Derivatives: Combine the derivatives to form the equation. 3x^(2) + 4y(dy)/(dx) - y - x(dy)/(dx) = 0Solve for dy/dx: Solve for (dy)/(dx). 4y(dy)/(dx) - x(dy)/(dx) = y - 3x^(2) (dy)/(dx)(4y - x) = y - 3x^(2) (dy)/(dx) = (y - 3x^(2)) / (4y - x)Plug in Point: Plug in the point (0,-1) into the equation. (dy)/(dx) = ((-1) - 3(0)^(2)) / (4(-1) - 0) (dy)/(dx) = (-1) / (-4) (dy)/(dx) = 1/4

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x^(3)+2y^(2)-xy=2
Find the value of
(dy)/(dx) at the point
(0,-1).
Choose 1 answer:
(A) 4
(B)
-(1)/(4)
(C)
(1)/(4)
(D) -4

$x^{3}+2 y^{2}-x y=2$ $\newline$ Find the value of $\frac{d y}{d x}$ at the point $(0,-1)$ . $\newline$ Choose $1$ answer: $\newline$ (A) $4$ $\newline$ (B) $-\frac{1}{4}$ $\newline$ (C) $\frac{1}{4}$ $\newline$ (D) $-4$

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Calculus

Find derivatives of using multiple formulae

Full solution

x^{3}+2 y^{2}-x y=2

\newline

Find the value of

\frac{d y}{d x}

at the point

(0,-1)

\newline

Choose

1

answer:

\newline

(A)

4

\newline

(B)

-\frac{1}{4}

\newline

(C)

\frac{1}{4}

\newline

(D)

-4

Differentiate Implicitly: Implicitly differentiate both sides of the equation with respect to $x$ . $\frac{d}{dx}(x^{3}+2y^{2}-xy) = \frac{d}{dx}(2)$
Differentiate Terms: Differentiate each term separately. $\frac{d}{dx}(x^{3}) = 3x^{2}$ , $\frac{d}{dx}(2y^{2}) = 4y\frac{dy}{dx}$ , $\frac{d}{dx}(-xy) = -y - x\frac{dy}{dx}$ , $\frac{d}{dx}(2) = 0$
Combine Derivatives: Combine the derivatives to form the equation. $3x^{2} + 4y\frac{dy}{dx} - y - x\frac{dy}{dx} = 0$
Solve for $\frac{dy}{dx}$ : Solve for $\frac{dy}{dx}$ . $4y\frac{dy}{dx} - x\frac{dy}{dx} = y - 3x^{2}$ $\frac{dy}{dx}(4y - x) = y - 3x^{2}$ $\frac{dy}{dx} = \frac{y - 3x^{2}}{4y - x}$
Plug in Point: Plug in the point $(0,-1)$ into the equation. $\newline$ $(\frac{dy}{dx}) = \frac{((-1) - 3(0)^{2})}{(4(-1) - 0)}$ $\newline$ $(\frac{dy}{dx}) = \frac{(-1)}{(-4)}$ $\newline$ $(\frac{dy}{dx}) = \frac{1}{4}$