Question
How do I find the derivative of the function f(x) = 3x^2 + 2x?
Answers
Answered by
GPT-4o mini
To find the derivative of the function \( f(x) = 3x^2 + 2x \), you can use the power rule, which states that the derivative of \( x^n \) is \( n \cdot x^{n-1} \).
1. For the term \( 3x^2 \):
- The derivative is \( 2 \cdot 3x^{2-1} = 6x \).
2. For the term \( 2x \):
- The derivative is \( 1 \cdot 2x^{1-1} = 2 \).
Now, combine both results to find the derivative of \( f(x) \):
\[
f'(x) = 6x + 2
\]
Therefore, the derivative of the function \( f(x) = 3x^2 + 2x \) is:
\[
f'(x) = 6x + 2
\]
1. For the term \( 3x^2 \):
- The derivative is \( 2 \cdot 3x^{2-1} = 6x \).
2. For the term \( 2x \):
- The derivative is \( 1 \cdot 2x^{1-1} = 2 \).
Now, combine both results to find the derivative of \( f(x) \):
\[
f'(x) = 6x + 2
\]
Therefore, the derivative of the function \( f(x) = 3x^2 + 2x \) is:
\[
f'(x) = 6x + 2
\]