If 3y^(2)-4x^(3)=3x^(2) 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: 3y^(2)-4x^(3)=3x^(2). We will use implicit differentiation because y is a function of x.Differentiate with Respect: Differentiate both sides of the equation with respect to x. The left side of the equation, 3y^(2), becomes 6y(dy/dx) because of the chain rule. The term -4x^(3) becomes -12x^(2). The right side of the equation, 3x^(2), becomes 6x.Write Differentiated Equation: Write down the differentiated equation. 6y(dy/dx) - 12x^(2) = 6xIsolate Term with dy/dx: Isolate the term with (dy/dx) on one side of the equation. 6y(dy/dx) = 12x^(2) + 6xDivide and Solve for dy/dx: Divide both sides of the equation by 6y to solve for (dy/dx). (dy/dx) = (12x^(2) + 6x) / (6y)Simplify Right Side: Simplify the right side of the equation. (dy/dx) = (2x^(2) + x) / y

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

If $3 y^{2}-4 x^{3}=3 x^{2}$ 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

3 y^{2}-4 x^{3}=3 x^{2}

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 $x$ : $3y^{2}-4x^{3}=3x^{2}$ . We will use implicit differentiation because $y$ is a function of $x$ .
Differentiate with Respect: Differentiate both sides of the equation with respect to $x$ . The left side of the equation, $3y^{2}$ , becomes $6y\frac{dy}{dx}$ because of the chain rule. The term $-4x^{3}$ becomes $-12x^{2}$ . The right side of the equation, $3x^{2}$ , becomes $6x$ .
Write Differentiated Equation: Write down the differentiated equation. $\newline$ $6y\frac{dy}{dx} - 12x^{2} = 6x$
Isolate Term with $\frac{dy}{dx}$ : Isolate the term with $\frac{dy}{dx}$ on one side of the equation. $\newline$ $6y\frac{dy}{dx} = 12x^{2} + 6x$
Divide and Solve for $\frac{dy}{dx}$ : Divide both sides of the equation by $6y$ to solve for $\frac{dy}{dx}$ . $\frac{dy}{dx} = \frac{12x^{2} + 6x}{6y}$
Simplify Right Side: Simplify the right side of the equation. $(\frac{dy}{dx}) = \frac{2x^{2} + x}{y}$