Derivatives Find and simplify the derivative of the following functions.
g(t) = 3t² + 6/t⁷

Verified step by step guidance

1. Step 1: Identify the function components. The function is g(t) = 3t^2 + 6/t^7. It consists of two terms: 3t^2 and 6/t^7.
2. Step 2: Rewrite the function for easier differentiation. The term 6/t^7 can be rewritten using negative exponents as 6t^(-7). So, g(t) = 3t^2 + 6t^(-7).
3. Step 3: Differentiate each term separately. Use the power rule for differentiation, which states that the derivative of t^n is n*t^(n-1).
4. Step 4: Apply the power rule to the first term. The derivative of 3t^2 is 2*3*t^(2-1) = 6t.
5. Step 5: Apply the power rule to the second term. The derivative of 6t^(-7) is -7*6*t^(-7-1) = -42t^(-8).