Questions: Find the differential of the function. y = sqrt(3 - t^6) dy =

Solution Steps

To find the differential of the function \( y = \sqrt{3 - t^6} \), we need to apply the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function times the derivative of the inner function. Here, the outer function is the square root, and the inner function is \( 3 - t^6 \).

We start with the function given by \[ y = \sqrt{3 - t^6}. \]

To find the differential \( dy \), we need to compute the derivative \( \frac{dy}{dt} \) using the chain rule. The derivative is given by: \[ \frac{dy}{dt} = -\frac{3t^5}{\sqrt{3 - t^6}}. \]

The differential \( dy \) can be expressed as: \[ dy = \frac{dy}{dt} \, dt = -\frac{3t^5}{\sqrt{3 - t^6}} \, dt. \]

Final Answer