Problem 22 - College Algebra and Calculus: An Applied Approach

Question

Find the derivative of the function. $$ s(t)=4 t^{-1}+1 $$

Step-by-Step Solution

Answer

The derivative of \(s(t) = 4 t^{-1} + 1\) is \(s'(t) = -4 t^{-2}\).

Step 1: Identify the function's terms

The function has two terms: \(4t^{-1}\) and \(1\). The power rule will be applied to the first term, and the constant will be considered for the second.

Step 2: Apply the power rule

Apply the power rule to \(4t^{-1}\). Multiply the coefficient by the current exponent to get the new coefficient, and subtract 1 from the current exponent to get the new exponent: \(-4 t^{-2}\).

Step 3: Consider the constant term

The derivative of a constant is 0, so the derivative of the second term is 0.

Step 4: Combine the terms

Combine the derivative of the first term and the derivative of the second term to get the overall derivative: \(-4 t^{-2} + 0\), which simplifies to \(-4 t^{-2}\).