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

Identify Equation: Identify the equation that needs to be differentiated with respect to x. -5x - 3xy + y^(2) = 0 We will use implicit differentiation to find (dy)/(dx).Differentiate with Respect: Differentiate both sides of the equation with respect to x. The derivative of -5x with respect to x is -5. The derivative of -3xy with respect to x is -3y - 3x(dy/dx) because it is a product of two functions (use the product rule). The derivative of y^(2) with respect to x is 2y(dy/dx) because it is a function of y (use the chain rule). The derivative of 0 with respect to x is 0. So, we have -5 - 3y - 3x(dy/dx) + 2y(dy/dx) = 0.Combine and Solve: Combine like terms and solve for (dy)/(dx). -5 - 3y = 3x(dy/dx) - 2y(dy/dx) Group the terms with (dy/dx) on one side of the equation. (3x - 2y)(dy/dx) = 5 + 3yIsolate (dy/dx): Divide both sides by (3x - 2y) to isolate (dy/dx). (dy/dx) = (5 + 3y) / (3x - 2y)

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

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

Full solution

Q. If

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

then find

\frac{d y}{d x}

in terms of

x

and

y

\newline

Answer:

\frac{d y}{d x}=

Identify Equation: Identify the equation that needs to be differentiated with respect to $x$ . $-5x - 3xy + y^{2} = 0$ We will use implicit differentiation to find $\frac{dy}{dx}$ .
Differentiate with Respect: Differentiate both sides of the equation with respect to $x$ . The derivative of $-5x$ with respect to $x$ is $-5$ . The derivative of $-3xy$ with respect to $x$ is $-3y - 3x\frac{dy}{dx}$ because it is a product of two functions (use the product rule). The derivative of $y^{2}$ with respect to $x$ is $2y\frac{dy}{dx}$ because it is a function of $-5x$ $0$ (use the chain rule). The derivative of $-5x$ $1$ with respect to $x$ is $-5x$ $1$ . So, we have $-5x$ $4$ .
Combine and Solve: Combine like terms and solve for $\frac{dy}{dx}$ . $-5 - 3y = 3x\frac{dy}{dx} - 2y\frac{dy}{dx}$ Group the terms with $\frac{dy}{dx}$ on one side of the equation. $(3x - 2y)\frac{dy}{dx} = 5 + 3y$
Isolate $(\frac{dy}{dx}):</b> Divide both sides by \$(3x - 2y)$ to isolate (\frac{dy}{dx}).$\newline\$(\frac{dy}{dx}) = \frac{5 + 3y}{3x - 2y}$

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