If -y^(2)-x^(3)+4+5x=0 then find (dy)/(dx) in terms of x and y. Answer: (dy)/(dx)=

Given Equation: We are given the equation -y^2 - x^3 + 4 + 5x = 0. To find (dy)/(dx), we will differentiate both sides of the equation with respect to x, treating y as an implicit function of x.Differentiate -y^2: Differentiate -y^2 with respect to x. Since y is a function of x, we use the chain rule: -2y * (dy)/(dx).Differentiate -x^3: Differentiate -x^3 with respect to x. The derivative is -3x^2.Differentiate 4: Differentiate 4 with respect to x. The derivative of a constant is 0.Differentiate 5x: Differentiate 5x with respect to x. The derivative is 5.Combine Derivatives: Combine all the derivatives to rewrite the differentiated equation: -2y * (dy)/(dx) - 3x^2 + 0 + 5 = 0.Isolate (dy)/(dx): Now, we solve for (dy)/(dx). First, we isolate the term with (dy)/(dx) on one side: -2y * (dy)/(dx) = 3x^2 - 5.Solve for (dy)/(dx): Divide both sides by -2y to solve for (dy)/(dx): (dy)/(dx) = (3x^2 - 5) / (-2y).

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If
-y^(2)-x^(3)+4+5x=0 then find
(dy)/(dx) in terms of
x and
y.
Answer:
(dy)/(dx)=

If $-y^{2}-x^{3}+4+5 x=0$ then find $\frac{d y}{d x}$ in terms of $x$ and $y$ . $\newline$ Answer: $\frac{d y}{d x}=$

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Algebra 2

Evaluate exponential functions

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Q. If

-y^{2}-x^{3}+4+5 x=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 $-y^2 - x^3 + 4 + 5x = 0$ . To find $\frac{dy}{dx}$ , we will differentiate both sides of the equation with respect to $x$ , treating $y$ as an implicit function of $x$ .
Differentiate $-y^2$ : Differentiate $-y^2$ with respect to $x$ . Since $y$ is a function of $x$ , we use the chain rule: $-2y \cdot \frac{dy}{dx}$ .
Differentiate $-x^3$ : Differentiate $-x^3$ with respect to $x$ . The derivative is $-3x^2$ .
Differentiate $4$ : Differentiate $4$ with respect to $x$ . The derivative of a constant is $0$ .
Differentiate $5x$ : Differentiate $5x$ with respect to $x$ . The derivative is $5$ .
Combine Derivatives: Combine all the derivatives to rewrite the differentiated equation: $-2y \cdot \frac{dy}{dx} - 3x^2 + 0 + 5 = 0$ .
Isolate $(dy)/(dx)$ : Now, we solve for $(dy)/(dx)$ . First, we isolate the term with $(dy)/(dx)$ on one side: $-2y \cdot (dy)/(dx) = 3x^2 - 5$ .
Solve for $(\frac{dy}{dx}):</b> Divide both sides by \$-2y$ to solve for $(\frac{dy}{dx}): \$\frac{dy}{dx} = \frac{3x^2 - 5}{-2y}$ .

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If −y2−x3+4+5x=0 -y^{2}-x^{3}+4+5 x=0 −y2−x3+4+5x=0 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 $-y^{2}-x^{3}+4+5 x=0$ then find $\frac{d y}{d x}$ in terms of $x$ and $y$ . $\newline$ Answer: $\frac{d y}{d x}=$