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Find d y / d t if y= ³(π-t).

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Final answer:

The derivative of y with respect to t is -(3/2) * √(π - t)

Step-by-step explanation:

The question asks to find the derivative of y with respect to t, given that y = √(π - t)3.

To find the derivative, we can use the chain rule. Let u = π - t. So, y = u3/2. Taking the derivative of y with respect to t, we get:

dy/dt = (dy/du) * (du/dt)

Using the power rule, dy/du = (3/2) * u1/2. And du/dt = -1

Substituting these values, dy/dt = (3/2) * u1/2 * (-1) = -(3/2) * √(π - t)

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