Questions: Find the differential (d y) of the given function. [ y=6 x^2-5 ] (d y=)

Solution Steps

To find the differential $dy$ of the given function $y = 6x^2 - 5$, we need to compute the derivative of $y$ with respect to $x$ and then multiply by $dx$.

We start with the function given by $$y = 6x^2 - 5.$$

Next, we compute the derivative of $y$ with respect to $x$: $$\frac{dy}{dx} = \frac{d}{dx}(6x^2 - 5) = 12x.$$

The differential $dy$ can be expressed as: $$dy = \frac{dy}{dx} \cdot dx = 12x \cdot dx.$$

Final Answer