If 3-5y+xy=0 then find (dy)/(dx) in terms of x and y. Answer: (dy)/(dx)=

Given Equation: We are given the equation 3 - 5y + xy = 0, and we need to find the derivative of y with respect to x, denoted as (dy)/(dx). To do this, we will use implicit differentiation, which involves taking the derivative of both sides of the equation with respect to x, while treating y as a function of x.Implicit Differentiation: First, we differentiate each term of the equation with respect to x. The derivative of the constant 3 with respect to x is 0. The derivative of -5y with respect to x is -5(dy/dx), since y is a function of x. The derivative of xy with respect to x is y + x(dy/dx) by using the product rule (d(uv)/dx = u(dv/dx) + v(du/dx), where u = x and v = y).Differentiate Terms: Now we write the differentiated equation: 0 - 5(dy/dx) + y + x(dy/dx) = 0.Write Differentiated Equation: Next, we combine like terms to solve for (dy/dx). This gives us: -5(dy/dx) + x(dy/dx) = -y.Combine Like Terms: We factor out (dy/dx) from the left side of the equation: (dy/dx)(-5 + x) = -y.Factor Out: Now, we solve for (dy/dx) by dividing both sides of the equation by (-5 + x): (dy/dx) = -y / (-5 + x).

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If
3-5y+xy=0 then find
(dy)/(dx) in terms of
x and
y.
Answer:
(dy)/(dx)=

If $3-5 y+x y=0$ 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

3-5 y+x y=0

then find

\frac{d y}{d x}

in terms of

x

and

y

\newline

Answer:

\frac{d y}{d x}=

Given Equation: We are given the equation $3 - 5y + xy = 0$ , and we need to find the derivative of $y$ with respect to $x$ , denoted as $\frac{dy}{dx}$ . To do this, we will use implicit differentiation, which involves taking the derivative of both sides of the equation with respect to $x$ , while treating $y$ as a function of $x$ .
Implicit Differentiation: First, we differentiate each term of the equation with respect to $x$ . The derivative of the constant $3$ with respect to $x$ is $0$ . The derivative of $-5y$ with respect to $x$ is $-5\frac{dy}{dx}$ , since $y$ is a function of $x$ . The derivative of $xy$ with respect to $x$ is $3$ $1$ by using the product rule ( $3$ $2$ , where $3$ $3$ and $3$ $4$ ).
Differentiate Terms: Now we write the differentiated equation: $0 - 5\frac{dy}{dx} + y + x\frac{dy}{dx} = 0$ .
Write Differentiated Equation: Next, we combine like terms to solve for $\frac{dy}{dx}$ . This gives us: $-5\frac{dy}{dx} + x\frac{dy}{dx} = -y$ .
Combine Like Terms: We factor out $\frac{dy}{dx}$ from the left side of the equation: $\left(\frac{dy}{dx}\right)(-5 + x) = -y$ .
Factor Out: Now, we solve for $\frac{dy}{dx}$ by dividing both sides of the equation by $(-5 + x)$ : $\frac{dy}{dx} = \frac{-y}{-5 + x}$ .