If -2y-1-x=-xy then find (dy)/(dx) in terms of x and y. Answer: (dy)/(dx)=

Differentiate left side with respect to x: We are given the equation -2y - 1 - x = -xy. To find (dy)/(dx), we need to differentiate both sides of the equation with respect to x, treating y as a function of x (implicit differentiation).Differentiate right side with respect to x: Differentiate the left side of the equation with respect to x. The derivative of -2y with respect to x is -2(dy/dx) because y is a function of x. The derivative of -1 with respect to x is 0, and the derivative of -x with respect to x is -1.Combine differentiated equations: Differentiate the right side of the equation with respect to x. The derivative of -xy with respect to x is -y - x(dy/dx) because we use the product rule for differentiation (d/dx of u*v = u*(dv/dx) + v*(du/dx), where u = -y and v = x).Isolate terms with (dy/dx): Now we have the differentiated equation: -2(dy/dx) - 1 = -y - x(dy/dx).Add x(dy/dx) and 1: We need to solve for (dy/dx). To do this, we'll collect all the terms involving (dy/dx) on one side of the equation and the constant terms on the other side.Combine like terms: Add x(dy/dx) to both sides and add 1 to both sides to isolate terms with (dy/dx) on one side: -2(dy/dx) + x(dy/dx) = -y + 1.Divide both sides to solve: Combine like terms: (-2 + x)(dy/dx) = -y + 1.Now, divide both sides by (-2 + x) to solve for (dy/dx): (dy/dx) = (-y + 1) / (-2 + x).

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If
-2y-1-x=-xy then find
(dy)/(dx) in terms of
x and
y.
Answer:
(dy)/(dx)=

If $-2 y-1-x=-x y$ then find $\frac{d y}{d x}$ in terms of $x$ and $y$ . $\newline$ Answer: $\frac{d y}{d x}=$

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Q. If

-2 y-1-x=-x y

then find

\frac{d y}{d x}

in terms of

x

and

y

\newline

Answer:

\frac{d y}{d x}=

Differentiate left side with respect to $x$ : We are given the equation $-2y - 1 - x = -xy$ . To find $\frac{dy}{dx}$ , we need to differentiate both sides of the equation with respect to $x$ , treating $y$ as a function of $x$ (implicit differentiation).
Differentiate right side with respect to $x$ : Differentiate the left side of the equation with respect to $x$ . The derivative of $-2y$ with respect to $x$ is $-2\frac{dy}{dx}$ because $y$ is a function of $x$ . The derivative of $-1$ with respect to $x$ is $0$ , and the derivative of $x$ $0$ with respect to $x$ is $-1$ .
Combine differentiated equations: Differentiate the right side of the equation with respect to $x$ . The derivative of $-xy$ with respect to $x$ is $-y - x(\frac{dy}{dx})$ because we use the product rule for differentiation ( $\frac{d}{dx}$ of $u\cdot v = u\cdot(\frac{dv}{dx}) + v\cdot(\frac{du}{dx})$ , where $u = -y$ and $v = x$ ).
Isolate terms with (\frac{dy}{dx}): Now we have the differentiated equation: \(\(-2(\frac{dy}{dx}) - $1$ = -y - x(\frac{dy}{dx}).
Add $x\frac{dy}{dx}$ and $1$ : We need to solve for $\frac{dy}{dx}$ . To do this, we'll collect all the terms involving $\frac{dy}{dx}$ on one side of the equation and the constant terms on the other side.
Combine like terms: Add $x\frac{dy}{dx}$ to both sides and add $1$ to both sides to isolate terms with $\frac{dy}{dx}$ on one side: $-2\frac{dy}{dx} + x\frac{dy}{dx} = -y + 1$ .
Divide both sides to solve: Combine like terms: $(-2 + x)(\frac{dy}{dx}) = -y + 1$ .
Divide both sides to solve: Combine like terms: $(-2 + x)(\frac{dy}{dx}) = -y + 1$ .Now, divide both sides by $(-2 + x)$ to solve for $(\frac{dy}{dx})$ : $(\frac{dy}{dx}) = \frac{-y + 1}{-2 + x}$ .