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

Differentiation with Product Rule: We are given the equation xy + 5y^2 - x^3 = 0. To find (dy)/(dx), we will differentiate both sides of the equation with respect to x, using implicit differentiation.Differentiation with Chain Rule: Differentiate xy with respect to x. Using the product rule, the derivative of xy with respect to x is y + x(dy)/(dx).Differentiation of -x^3: Differentiate 5y^2 with respect to x. Since y is a function of x, we use the chain rule. The derivative of 5y^2 with respect to x is 10y(dy)/(dx).Combining Derivatives: Differentiate -x^3 with respect to x. The derivative of -x^3 with respect to x is -3x^2.Isolating (dy)/(dx): Combine the derivatives from the previous steps to rewrite the differentiated equation: y + x(dy)/(dx) + 10y(dy)/(dx) - 3x^2 = 0.Now, we need to solve for (dy)/(dx). First, move all terms not containing (dy)/(dx) to the other side of the equation: x(dy)/(dx) + 10y(dy)/(dx) = 3x^2 - y.Factor out (dy)/(dx) from the left side of the equation: (dy)/(dx)(x + 10y) = 3x^2 - y.Divide both sides of the equation by (x + 10y) to isolate (dy)/(dx): (dy)/(dx) = (3x^2 - y) / (x + 10y).

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

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

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

then find

\frac{d y}{d x}

in terms of

x

and

y

\newline

Answer:

\frac{d y}{d x}=

Differentiation with Product Rule: We are given the equation $xy + 5y^2 - x^3 = 0$ . To find $\frac{dy}{dx}$ , we will differentiate both sides of the equation with respect to $x$ , using implicit differentiation.
Differentiation with Chain Rule: Differentiate $xy$ with respect to $x$ . Using the product rule, the derivative of $xy$ with respect to $x$ is $y + x\frac{dy}{dx}$ .
Differentiation of $-x^3$ : Differentiate $5y^2$ with respect to $x$ . Since $y$ is a function of $x$ , we use the chain rule. The derivative of $5y^2$ with respect to $x$ is $10y\frac{dy}{dx}$ .
Combining Derivatives: Differentiate $-x^3$ with respect to $x$ . The derivative of $-x^3$ with respect to $x$ is $-3x^2$ .
Isolating $(\frac{dy}{dx}):$ Combine the derivatives from the previous steps to rewrite the differentiated equation: $y + x(\frac{dy}{dx}) + 10y(\frac{dy}{dx}) - 3x^2 = 0$ .
Isolating $(dy)/(dx)$ : Combine the derivatives from the previous steps to rewrite the differentiated equation: $y + x(dy)/(dx) + 10y(dy)/(dx) - 3x^2 = 0$ .Now, we need to solve for $(dy)/(dx)$ . First, move all terms not containing $(dy)/(dx)$ to the other side of the equation: $x(dy)/(dx) + 10y(dy)/(dx) = 3x^2 - y$ .
Isolating $(\frac{dy}{dx}):</b> Combine the derivatives from the previous steps to rewrite the differentiated equation: \$y + x\frac{dy}{dx} + 10y\frac{dy}{dx} - 3x^2 = 0$ .Now, we need to solve for $\frac{dy}{dx}$ . First, move all terms not containing $\frac{dy}{dx}$ to the other side of the equation: $x\frac{dy}{dx} + 10y\frac{dy}{dx} = 3x^2 - y$ .Factor out $\frac{dy}{dx}$ from the left side of the equation: $\frac{dy}{dx}(x + 10y) = 3x^2 - y$ .
Isolating $(dy)/(dx)$ : Combine the derivatives from the previous steps to rewrite the differentiated equation: $y + x(dy)/(dx) + 10y(dy)/(dx) - 3x^2 = 0$ .Now, we need to solve for $(dy)/(dx)$ . First, move all terms not containing $(dy)/(dx)$ to the other side of the equation: $x(dy)/(dx) + 10y(dy)/(dx) = 3x^2 - y$ .Factor out $(dy)/(dx)$ from the left side of the equation: $(dy)/(dx)(x + 10y) = 3x^2 - y$ .Divide both sides of the equation by $(x + 10y)$ to isolate $(dy)/(dx)$ : $(dy)/(dx) = (3x^2 - y) / (x + 10y)$ .

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