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

Implicit Differentiation: To find the derivative (dy)/(dx), we need to differentiate the given equation implicitly with respect to x. Differentiate each term of the equation -5x^(3) - xy + 3 - 2y = 0 with respect to x. For -5x^(3), the derivative is -15x^(2). For -xy, we apply the product rule: the derivative is -y - x(dy/dx). For the constant 3, the derivative is 0. For -2y, the derivative is -2(dy/dx) because y is a function of x.Derivative Calculation: Combine the derivatives to form the differentiated equation. -15x^(2) - y - x(dy/dx) - 2(dy/dx) = 0 Group the terms with (dy/dx) on one side and the rest on the other side. -x(dy/dx) - 2(dy/dx) = 15x^(2) + y Factor out (dy/dx) from the left side. (dy/dx)(-x - 2) = 15x^(2) + yCombining Derivatives: Solve for (dy/dx) by dividing both sides by (-x - 2). (dy/dx) = (15x^(2) + y) / (-x - 2) This gives us the derivative of y with respect to x in terms of x and y.

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

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

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

then find

\frac{d y}{d x}

in terms of

x

and

y

\newline

Answer:

\frac{d y}{d x}=

Implicit Differentiation: To find the derivative $\frac{dy}{dx}$ , we need to differentiate the given equation implicitly with respect to $x$ . Differentiate each term of the equation $-5x^{3} - xy + 3 - 2y = 0$ with respect to $x$ . For $-5x^{3}$ , the derivative is $-15x^{2}$ . For $-xy$ , we apply the product rule: the derivative is $-y - x\frac{dy}{dx}$ . For the constant $3$ , the derivative is $0$ . For $x$ $0$ , the derivative is $x$ $1$ because $x$ $2$ is a function of $x$ .
Derivative Calculation: Combine the derivatives to form the differentiated equation. $\newline$ $-15x^{2} - y - x\frac{dy}{dx} - 2\frac{dy}{dx} = 0$ $\newline$ Group the terms with $\frac{dy}{dx}$ on one side and the rest on the other side. $\newline$ $-x\frac{dy}{dx} - 2\frac{dy}{dx} = 15x^{2} + y$ $\newline$ Factor out $\frac{dy}{dx}$ from the left side. $\newline$ $\frac{dy}{dx}(-x - 2) = 15x^{2} + y$
Combining Derivatives: Solve for $(\frac{dy}{dx})$ by dividing both sides by $(-x - 2)$ . $\newline$ $(\frac{dy}{dx}) = \frac{15x^{2} + y}{-x - 2}$ $\newline$ This gives us the derivative of $y$ with respect to $x$ in terms of $x$ and $y$ .