Problem 17 - College Algebra and Calculus: An Applied Approach

Question

Find the derivative of the function. $$ y=4 t^{4 / 3} $$

Step-by-Step Solution

Answer

The derivative of the function \(y = 4t^{4/3}\) is \(y' = (16/3)t^{1/3}\)

Step 1: Identify the function

In this case, the function to be derived is \(y = 4t^{4/3}\)

Step 2: Apply the power rule

We want to apply the power rule of differentiation which states that if \(y = ax^n\), then the derivative \(y' = nax^{n-1}\). Thus, applying the power rule to our function we get, \(y'=(4/3)*4t^{4/3-1} = (16/3)t^{1/3}\).

Step 3: Simplify the derivative

The derivative \(y' = (16/3)t^{1/3}\) is already simplified.