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

Rewrite Equation: First, we need to rewrite the given equation to make it easier to differentiate with respect to x. The equation is -x^(2) + 2y^(3) + 3y = y^(2) + 5.Differentiate with Respect to x: Now, we will differentiate both sides of the equation with respect to x. Remember that when differentiating terms with y, we treat y as a function of x and use the chain rule to include (dy)/(dx).Left Side Differentiation: Differentiate the left side of the equation with respect to x: d/dx(-x^(2) + 2y^(3) + 3y). This gives us -2x + 2 * 3y^(2) * (dy)/(dx) + 3 * (dy)/(dx).Right Side Differentiation: Differentiate the right side of the equation with respect to x: d/dx(y^(2) + 5). This gives us 2y * (dy)/(dx) + 0, since the derivative of a constant is 0.Solve for (dy)/(dx): Now we have the following equation from the derivatives: -2x + 6y^(2) * (dy)/(dx) + 3 * (dy)/(dx) = 2y * (dy)/(dx).Collect Terms: We need to solve for (dy)/(dx). To do this, we'll collect all the terms with (dy)/(dx) on one side of the equation and the rest on the other side. This gives us 6y^(2) * (dy)/(dx) + 3 * (dy)/(dx) - 2y * (dy)/(dx) = 2x.Factor Out (dy)/(dx): Factor out (dy)/(dx) from the left side of the equation: (dy)/(dx) * (6y^(2) + 3 - 2y) = 2x.Isolate (dy)/(dx): Now, isolate (dy)/(dx) by dividing both sides of the equation by (6y^(2) + 3 - 2y): (dy)/(dx) = 2x / (6y^(2) + 3 - 2y).

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

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

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

then find

\frac{d y}{d x}

in terms of

x

and

y

\newline

Answer:

\frac{d y}{d x}=

Rewrite Equation: First, we need to rewrite the given equation to make it easier to differentiate with respect to $x$ . The equation is $-x^{2} + 2y^{3} + 3y = y^{2} + 5$ .
Differentiate with Respect to $x$ : Now, we will differentiate both sides of the equation with respect to $x$ . Remember that when differentiating terms with $y$ , we treat $y$ as a function of $x$ and use the chain rule to include $\frac{dy}{dx}$ .
Left Side Differentiation: Differentiate the left side of the equation with respect to $x$ : $\frac{d}{dx}(-x^{2} + 2y^{3} + 3y)$ . This gives us $-2x + 2 \times 3y^{2} \times \frac{dy}{dx} + 3 \times \frac{dy}{dx}$ .
Right Side Differentiation: Differentiate the right side of the equation with respect to $x$ : $\frac{d}{dx}(y^{2} + 5)$ . This gives us $2y \cdot \frac{dy}{dx} + 0$ , since the derivative of a constant is $0$ .
Solve for (\frac{dy}{dx}): Now we have the following equation from the derivatives: \(\(-2x + $6$ y^{ $2$ } \cdot (\frac{dy}{dx}) + $3$ \cdot (\frac{dy}{dx}) = $2$ y \cdot (\frac{dy}{dx}).
Collect Terms: We need to solve for $\frac{dy}{dx}$ . To do this, we'll collect all the terms with $\frac{dy}{dx}$ on one side of the equation and the rest on the other side. This gives us $6y^{2} \cdot \frac{dy}{dx} + 3 \cdot \frac{dy}{dx} - 2y \cdot \frac{dy}{dx} = 2x$ .
Factor Out $(\frac{dy}{dx}):</b> Factor out \$(\frac{dy}{dx})$ from the left side of the equation: $(\frac{dy}{dx}) \cdot (6y^{2} + 3 - 2y) = 2x$ .
Isolate $(\frac{dy}{dx}):</b> Now, isolate \$(\frac{dy}{dx})$ by dividing both sides of the equation by $(6y^{2} + 3 - 2y): \$\frac{dy}{dx} = \frac{2x}{6y^{2} + 3 - 2y}$ .

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If −x2+2y3+3y=y2+5 -x^{2}+2 y^{3}+3 y=y^{2}+5 −x2+2y3+3y=y2+5 then find dydx \frac{d y}{d x} dxdy​ in terms of x x x and y y y.\newlineAnswer: dydx= \frac{d y}{d x}= dxdy​=

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