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4x-x^(2)y+y^(3)=10
Find the value of
(dy)/(dx) at the point
(1,2).
Choose 1 answer:
(A) -4
(B)
(2)/(3)
(C) -1
(D) 0

$4 x-x^{2} y+y^{3}=10$ $\newline$ Find the value of $\frac{d y}{d x}$ at the point $(1,2)$ . $\newline$ Choose $1$ answer: $\newline$ (A) $-4$ $\newline$ (B) $\frac{2}{3}$ $\newline$ (C) $-1$ $\newline$ (D) $0$

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Full solution

Q.

4 x-x^{2} y+y^{3}=10

\newline

Find the value of

\frac{d y}{d x}

at the point

(1,2)

.

\newline

Choose

1

answer:

\newline

(A)

-4

\newline

(B)

\frac{2}{3}

\newline

(C)

-1

\newline

(D)

0

Plug in point $(1,2)$ : Now, plug in the point $(1,2)$ into the differentiated equation. $\newline$ $4 - 2(1)(2) - (1)^2\frac{dy}{dx} + 3(2)^2\frac{dy}{dx} = 0$ $\newline$ $4 - 4 - \frac{dy}{dx} + 12\frac{dy}{dx} = 0$
Simplify and solve for $\frac{dy}{dx}$ : Simplify the equation to solve for $\frac{dy}{dx}$ . $0 - \frac{dy}{dx} + 12\left(\frac{dy}{dx}\right) = 0$ $11\left(\frac{dy}{dx}\right) = 4$ $\frac{dy}{dx} = \frac{4}{11}$

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