Question

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

Short answer

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

Step-by-step solution

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.

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: \(-4 t^{-2}\).

Consider the constant term

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

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 \(-4 t^{-2}\).