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The problem asks for the first derivative of the function \( f(x) = 3x^2 + 5x \).

To find the derivative, we apply the power rule, which states that for any term \( ax^n \), the derivative is given by:

\[
\frac{d}{dx}[ax^n] = n \cdot ax^{n-1}
\]

### Derivative of each term:
1. For \( 3x^2 \):  
   \[
   \frac{d}{dx}[3x^2] = 2 \cdot 3x^{2-1} = 6x
   \]
2. For \( 5x \):  
   \[
   \frac{d}{dx}[5x] = 5
   \]

### Therefore, the first derivative of the function is:
\[
f'(x) = 6x + 5
\]

Would you like further details or explanations on any steps?

Here are 5 related questions to explore:
1. What would be the second derivative of \( f(x) = 3x^2 + 5x \)?
2. How do we find the derivative of more complex functions like polynomials of higher degrees?
3. What is the geometrical interpretation of the first derivative in calculus?
4. How do derivatives apply in real-world situations, such as physics or economics?
5. What is the difference between the first and second derivative in terms of motion?

**Tip:** When finding the derivative of a polynomial, apply the power rule to each term individually.

Diberikan fungsi f(x) = 3x^2 + 5x. Berapa turunan pertama dari fungsi tersebut?

Learn how to find the first derivative of the function f(x) = 3x^2 + 5x using the power rule. This problem demonstrates key calculus concepts and is suitable for students in Grades 10-12.

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