Let y be defined implicitly by the equation 6x^(3)+(8)/(y)=10". " Use implicit differentiation to find (dy)/(dx).

Differentiate 6x^3: To find the derivative (dy)/(dx) using implicit differentiation, we need to differentiate both sides of the equation with respect to x. The equation is 6x^3 + 8/y = 10.Differentiate 8/y: Differentiate 6x^3 with respect to x. The derivative of 6x^3 with respect to x is 18x^2.Differentiate 10: Differentiate 8/y with respect to x. Since y is a function of x, we need to use the chain rule. The derivative of 8/y with respect to x is -8/y^2 * dy/dx.Combine derivatives: Differentiate 10 with respect to x. The derivative of a constant is 0.Solve for dy/dx: Combine the derivatives from the previous steps to form the differentiated equation: 18x^2 - 8/y^2 * dy/dx = 0.Simplify dy/dx: Solve for dy/dx. To do this, we isolate dy/dx on one side of the equation. We get dy/dx = (18x^2 * y^2) / 8.Simplify the expression for dy/dx. We can simplify (18x^2 * y^2) / 8 to (9x^2 * y^2) / 4.

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Let
y be defined implicitly by the equation

6x^(3)+(8)/(y)=10". "
Use implicit differentiation to find
(dy)/(dx).

Let $y$ be defined implicitly by the equation $\newline$ $6 x^{3}+\frac{8}{y}=10 \text {. }$ $\newline$ Use implicit differentiation to find $\frac{d y}{d x}$ .

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Q. Let

y

be defined implicitly by the equation

\newline

6 x^{3}+\frac{8}{y}=10 \text {. }

\newline

Use implicit differentiation to find

\frac{d y}{d x}

Differentiate $6x^3$ : To find the derivative $\frac{dy}{dx}$ using implicit differentiation, we need to differentiate both sides of the equation with respect to $x$ . The equation is $6x^3 + \frac{8}{y} = 10$ .
Differentiate $\frac{8}{y}$ : Differentiate $6x^3$ with respect to $x$ . The derivative of $6x^3$ with respect to $x$ is $18x^2$ .
Differentiate $10$ : Differentiate $\frac{8}{y}$ with respect to $x$ . Since $y$ is a function of $x$ , we need to use the chain rule. The derivative of $\frac{8}{y}$ with respect to $x$ is $-\frac{8}{y^2} * \frac{dy}{dx}$ .
Combine derivatives: Differentiate $10$ with respect to $x$ . The derivative of a constant is $0$ .
Solve for $\frac{dy}{dx}$ : Combine the derivatives from the previous steps to form the differentiated equation: $18x^2 - \frac{8}{y^2} \cdot \frac{dy}{dx} = 0$ .
Simplify $\frac{dy}{dx}$ : Solve for $\frac{dy}{dx}$ . To do this, we isolate $\frac{dy}{dx}$ on one side of the equation. We get $\frac{dy}{dx} = \frac{18x^2 \cdot y^2}{8}$ .
Simplify $\frac{dy}{dx}$ : Solve for $\frac{dy}{dx}$ . To do this, we isolate $\frac{dy}{dx}$ on one side of the equation. We get $\frac{dy}{dx} = \frac{18x^2 \cdot y^2}{8}$ .Simplify the expression for $\frac{dy}{dx}$ . We can simplify $\frac{18x^2 \cdot y^2}{8}$ to $\frac{9x^2 \cdot y^2}{4}$ .