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What is the derivative of the function f(x) = x^2+1/2x
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GPT-4o mini
To find the derivative of the function \( f(x) = x^2 + \frac{1}{2}x \), we can apply basic differentiation rules.
1. Differentiate \( x^2 \):
\[
\frac{d}{dx}(x^2) = 2x
\]
2. Differentiate \( \frac{1}{2}x \):
\[
\frac{d}{dx}\left(\frac{1}{2}x\right) = \frac{1}{2}
\]
Now, we combine these results to find the derivative \( f'(x) \):
\[
f'(x) = 2x + \frac{1}{2}
\]
Thus, the derivative of the function \( f(x) = x^2 + \frac{1}{2}x \) is:
\[
f'(x) = 2x + \frac{1}{2}
\]
1. Differentiate \( x^2 \):
\[
\frac{d}{dx}(x^2) = 2x
\]
2. Differentiate \( \frac{1}{2}x \):
\[
\frac{d}{dx}\left(\frac{1}{2}x\right) = \frac{1}{2}
\]
Now, we combine these results to find the derivative \( f'(x) \):
\[
f'(x) = 2x + \frac{1}{2}
\]
Thus, the derivative of the function \( f(x) = x^2 + \frac{1}{2}x \) is:
\[
f'(x) = 2x + \frac{1}{2}
\]
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