Question If 4x^2-3=-3y^3 then find (dy)/(dx) in terms of x and y Answer Attempt 1 out of 3 (dy)/(dz)=

To find $\frac{dy}{dx}$, we need to differentiate both sides of the equation with respect to x. <br /><br />Differentiating the left side of the equation with respect to x, we get:<br /><br />$\frac{d}{dx}(4x^2 - 3) = 8x$<br /><br />Differentiating the right side of the equation with respect to x, we get:<br /><br />$\frac{d}{dx}(-3y^3) = -9y^2 \cdot \frac{dy}{dx}$<br /><br />Setting these two derivatives equal to each other, we have:<br /><br />$8x = -9y^2 \cdot \frac{dy}{dx}$<br /><br />Solving for $\frac{dy}{dx}$, we get:<br /><br />$\frac{dy}{dx} = -\frac{8x}{9y^2}$<br /><br />Therefore, the correct answer is $\frac{dy}{dx} = -\frac{8x}{9y^2}$.