x^(2)-3xy+y^(3)=3 Find the value of (dy)/(dx) at the point (1,2). Choose 1 answer: (A) (4)/(15) (B) (4)/(9) (C) (15)/(4) () (9)/(4)

Differentiate Equation: Differentiate the given equation with respect to x, using implicit differentiation. d/dx(x^2) - d/dx(3xy) + d/dx(y^3) = d/dx(3)Apply Product Rule: Differentiate each term separately. 2x - 3(d/dx(xy)) + 3y^2(dy/dx) = 0Substitute Values: Apply the product rule to d/dx(xy). 2x - 3(x(dy/dx) + y) + 3y^2(dy/dx) = 0Simplify Equation: Substitute x=1 and y=2 into the differentiated equation. 2(1) - 3((1)(dy/dx) + 2) + 3(2)^2(dy/dx) = 0Combine Like Terms: Simplify the equation. 2 - 3(dy/dx) - 6 + 12(dy/dx) = 0Solve for dy/dx: Combine like terms. 9(dy/dx) - 4 = 0Solve for dy/dx. dy/dx = 4/9

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x^(2)-3xy+y^(3)=3
Find the value of
(dy)/(dx) at the point
(1,2).
Choose 1 answer:
(A)
(4)/(15)
(B)
(4)/(9)
(C)
(15)/(4)
()
(9)/(4)

$x^{2}-3 x y+y^{3}=3$ $\newline$ Find the value of $\frac{d y}{d x}$ at the point $(1,2)$ . $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{4}{15}$ $\newline$ (B) $\frac{4}{9}$ $\newline$ (C) $\frac{15}{4}$ $\newline$ (D) $\frac{9}{4}$

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Math Problems

Precalculus

Operations with rational exponents

Full solution

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

\newline

Find the value of

\frac{d y}{d x}

at the point

(1,2)

\newline

Choose

1

answer:

\newline

(A)

\frac{4}{15}

\newline

(B)

\frac{4}{9}

\newline

(C)

\frac{15}{4}

\newline

(D)

\frac{9}{4}

Differentiate Equation: Differentiate the given equation with respect to $x$ , using implicit differentiation. $\newline$ $\frac{d}{dx}(x^2) - \frac{d}{dx}(3xy) + \frac{d}{dx}(y^3) = \frac{d}{dx}(3)$
Apply Product Rule: Differentiate each term separately. $\newline$ $2x - 3\frac{d}{dx}(xy) + 3y^2\frac{dy}{dx} = 0$
Substitute Values: Apply the product rule to $\frac{d}{dx}(xy)$ . $2x - 3(x\frac{dy}{dx} + y) + 3y^2\frac{dy}{dx} = 0$
Simplify Equation: Substitute $x=1$ and $y=2$ into the differentiated equation. $2(1) - 3((1)\frac{dy}{dx} + 2) + 3(2)^2\frac{dy}{dx} = 0$
Combine Like Terms: Simplify the equation. $\newline$ $2 - 3\frac{dy}{dx} - 6 + 12\frac{dy}{dx} = 0$
Solve for $\frac{dy}{dx}$ : Combine like terms. $9\left(\frac{dy}{dx}\right) - 4 = 0$
Solve for $\frac{dy}{dx}$ : Combine like terms. $9\left(\frac{dy}{dx}\right) - 4 = 0$ Solve for $\frac{dy}{dx}$ . $\frac{dy}{dx} = \frac{4}{9}$