If y^(2)+3x-5x^(2)=-3+2y then find (dy)/(dx) in terms of x and y. Answer: (dy)/(dx)=

Differentiate with respect to x: First, we need to differentiate both sides of the equation with respect to x. The equation is y^(2) + 3x - 5x^(2) = -3 + 2y.Apply chain rule: Differentiate y^(2) with respect to x using the chain rule. The derivative of y^(2) with respect to x is 2y * (dy/dx).Differentiate 3x: Differentiate 3x with respect to x. The derivative of 3x with respect to x is 3.Differentiate -5x^2: Differentiate -5x^(2) with respect to x. The derivative of -5x^(2) with respect to x is -10x.Differentiate -3: Differentiate -3 with respect to x. The derivative of a constant is 0.Apply constant multiple rule: Differentiate 2y with respect to x using the constant multiple rule. The derivative of 2y with respect to x is 2 * (dy/dx).Combine differentiated parts: Combine all the differentiated parts to form the derivative of the entire equation. This gives us 2y * (dy/dx) + 3 - 10x = 2 * (dy/dx).Solve for (dy/dx): Now, we need to solve for (dy/dx). Subtract 2 * (dy/dx) from both sides to get all the (dy/dx) terms on one side. This gives us 2y * (dy/dx) - 2 * (dy/dx) = -3 + 10x.Factor out (dy/dx): Factor out (dy/dx) from the left side of the equation. This gives us (dy/dx) * (2y - 2) = -3 + 10x.Divide to solve for (dy/dx): Divide both sides by (2y - 2) to solve for (dy/dx). This gives us (dy/dx) = (-3 + 10x) / (2y - 2).

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If
y^(2)+3x-5x^(2)=-3+2y then find
(dy)/(dx) in terms of
x and
y.
Answer:
(dy)/(dx)=

If $y^{2}+3 x-5 x^{2}=-3+2 y$ then find $\frac{d y}{d x}$ in terms of $x$ and $y$ . $\newline$ Answer: $\frac{d y}{d x}=$

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Algebra 2

Evaluate exponential functions

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Q. If

y^{2}+3 x-5 x^{2}=-3+2 y

then find

\frac{d y}{d x}

in terms of

x

and

y

\newline

Answer:

\frac{d y}{d x}=

Differentiate with respect to $x$ : First, we need to differentiate both sides of the equation with respect to $x$ . The equation is $y^{2} + 3x - 5x^{2} = -3 + 2y$ .
Apply chain rule: Differentiate $y^{2}$ with respect to $x$ using the chain rule. The derivative of $y^{2}$ with respect to $x$ is $2y \cdot \left(\frac{dy}{dx}\right)$ .
Differentiate $3x$ : Differentiate $3x$ with respect to $x$ . The derivative of $3x$ with respect to $x$ is $3$ .
Differentiate $-5x^2$ : Differentiate $-5x^{2}$ with respect to $x$ . The derivative of $-5x^{2}$ with respect to $x$ is $-10x$ .
Differentiate $-3$ : Differentiate $-3$ with respect to $x$ . The derivative of a constant is $0$ .
Apply constant multiple rule: Differentiate $2y$ with respect to $x$ using the constant multiple rule. The derivative of $2y$ with respect to $x$ is $2 \times \left(\frac{dy}{dx}\right)$ .
Combine differentiated parts: Combine all the differentiated parts to form the derivative of the entire equation. This gives us $2y \cdot \left(\frac{dy}{dx}\right) + 3 - 10x = 2 \cdot \left(\frac{dy}{dx}\right)$ .
Solve for (\frac{dy}{dx}): Now, we need to solve for \$(\frac{dy}{dx})\. Subtract \$2 \times (\frac{dy}{dx}) from both sides to get all the $(\frac{dy}{dx})$ terms on one side. This gives us \(2y \times (\frac{dy}{dx}) - $2$ \times (\frac{dy}{dx}) = $-3$ + $10$ x\.
Factor out $\frac{dy}{dx}$ : Factor out $\frac{dy}{dx}$ from the left side of the equation. This gives us $\frac{dy}{dx} \times (2y - 2) = -3 + 10x$ .
Divide to solve for $(\frac{dy}{dx}):$ Divide both sides by $(2y - 2)$ to solve for $(\frac{dy}{dx})$ . This gives us $(\frac{dy}{dx}) = \frac{-3 + 10x}{2y - 2}$ .