If y^(3)+5y-x^(2)+1=0 then find (dy)/(dx) in terms of x and y. Answer: (dy)/(dx)=

Implicit Differentiation: Differentiate both sides of the equation with respect to x. We will use implicit differentiation because y is a function of x. Differentiate y^3 with respect to x: 3y^2(dy/dx) Differentiate 5y with respect to x: 5(dy/dx) Differentiate -x^2 with respect to x: -2x Differentiate 1 with respect to x: 0Write Differentiated Equation: Write down the differentiated equation. 3y^2(dy/dx) + 5(dy/dx) - 2x = 0Solve for (dy/dx): Solve for (dy/dx). Factor out (dy/dx) from the terms that contain it: (dy/dx)(3y^2 + 5) = 2x Now, divide both sides by (3y^2 + 5) to isolate (dy/dx): (dy/dx) = 2x / (3y^2 + 5)

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If
y^(3)+5y-x^(2)+1=0 then find
(dy)/(dx) in terms of
x and
y.
Answer:
(dy)/(dx)=

If $y^{3}+5 y-x^{2}+1=0$ 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 1

Transformations of quadratic functions

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Q. If

y^{3}+5 y-x^{2}+1=0

then find

\frac{d y}{d x}

in terms of

x

and

y

\newline

Answer:

\frac{d y}{d x}=

Implicit Differentiation: Differentiate both sides of the equation with respect to $x$ . We will use implicit differentiation because $y$ is a function of $x$ . Differentiate $y^3$ with respect to $x$ : $3y^2(\frac{dy}{dx})$ Differentiate $5y$ with respect to $x$ : $5(\frac{dy}{dx})$ Differentiate $-x^2$ with respect to $x$ : $y$ $1$ Differentiate $y$ $2$ with respect to $x$ : $y$ $4$
Write Differentiated Equation: Write down the differentiated equation. $\newline$ $3y^2\frac{dy}{dx} + 5\frac{dy}{dx} - 2x = 0$
Solve for (\frac{dy}{dx}): Solve for $(\frac{dy}{dx}).\(\newlineFactor out (\frac{dy}{dx}) from the terms that contain it:\(\newline(\frac{dy}{dx})(\(3y^ $2$ + $5$ ) = $2$ x $\newline$ Now, divide both sides by (\(3y^ $2$ + $5$ ) to isolate (\frac{dy}{dx}):\(\newline\((\frac{dy}{dx}) = \frac{\(2$x}{$3$y^$2$ + $5$}