Problem 12 - College Algebra and Calculus: An Applied Approach

Question

Find the derivative of the function. $$ y=t^{2}-6 $$

Step-by-Step Solution

Answer

The derivative of the function \(y = t^{2} - 6\) is \(2t\).

Step 1: Identify the function and its components

In the function \(y = t^{2} - 6\), the term \(t^{2}\) is a power function and \(-6\) is a constant.

Step 2: Applying the power rule

By applying the power rule, which states the derivative of \(t^n\) is \(n*\t^{n-1}\), to the term \(t^{2}\), the derivative is \(2t^{(2-1)} = 2t\).

Step 3: Differentiating the constant

The derivative of a constant is always zero. Hence, the derivative of \(-6\) is zero.

Step 4: Compile the total derivative

Combine the derivatives from Step 2 and Step 3 to find the total derivative of the function \(y = t^{2} - 6\). The derivative of the function is \(2t - 0 = 2t\).