What is the derivative of the function f(x) = x^2+1/2x

Answer 1

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: \[ f'(x) = 2x + \frac{1}{2} \]