Find $\frac{d y}{d x}$ using implicit differentiation.
\[
5 x^{3}=7 y^{2}-5 y
\]
\[
\frac{d y}{d x}=\square
\]

Answer

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Answer

Final Answer: The derivative of $y$ with respect to $x$ is $\boxed{\frac{15x^2}{14y - 5}}$.

Steps

Step 1 ：Given the equation $5 x^{3}=7 y^{2}-5 y$, we are asked to find $\frac{d y}{d x}$ using implicit differentiation.

Step 2 ：Differentiate both sides of the equation with respect to $x$. This gives us the equation $15x^2 = (14y - 5) \cdot \frac{dy}{dx}$.

Step 3 ：Solve the equation for $\frac{dy}{dx}$. This gives us $\frac{dy}{dx} = \frac{15x^2}{14y - 5}$.

Step 4 ：Final Answer: The derivative of $y$ with respect to $x$ is $\boxed{\frac{15x^2}{14y - 5}}$.