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

Transcript text: Find the differential $d y$ of the given function. \[ y=6 x^{2}-5 \] $d y=$

Solution

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 $.

Step 1: Define the Function

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

Step 2: Compute the Derivative

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

Step 3: Express the Differential

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

Final Answer

Thus, the differential $ dy $ is given by \[ \boxed{dy = 12x \, dx}. \]

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