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We are tasked with differentiating the function:

\[
g(t) = 7t + 6t^2
\]

Let's find the derivative \( g'(t) \).

1. The derivative of \( 7t \) with respect to \( t \) is \( 7 \).
2. The derivative of \( 6t^2 \) with respect to \( t \) is found using the power rule, which states that the derivative of \( t^n \) is \( n \cdot t^{n-1} \). Applying this rule, the derivative of \( 6t^2 \) is \( 12t \).

Therefore, the derivative of the function is:

\[
g'(t) = 7 + 12t
\]

Would you like further details or have any questions?

Here are 5 related questions:
1. What is the derivative of \( g(t) = 3t^3 + 2t + 5 \)?
2. How would you find the second derivative of \( g(t) = 7t + 6t^2 \)?
3. What is the derivative of a constant function like \( g(t) = 9 \)?
4. How does the chain rule apply to more complex functions?
5. What is the geometric interpretation of the derivative of a function?

**Tip:** When differentiating polynomial terms, use the power rule to bring down the exponent and reduce it by one.

Differentiate the function: g(t) = 7t + 6t^2

Learn how to differentiate the function g(t) = 7t + 6t^2. This problem involves key calculus concepts, including the power rule for derivatives. Suitable for students in Grades 11-12.

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