# How do you find the derivative of f(x)=1/4x^2-x+4?

Dec 17, 2017

$\frac{1}{2} x - 1$

#### Explanation:

To find the derivative of a polynomial, we can use the sum/difference rules for differentiation, which means that we can take the derivative of each term separated by an addition/subtraction sign separately.

First, let's find the derivative of the first term by using the power rule, which states that the derivative of ${x}^{n}$ is $n {x}^{n - 1}$:

When there's a constant in front of a variable, just put the constant to the side for the moment and focus on differentiating the non-constant variable. After that is done, the constant should be multiplied by the new derivative that is obtained.

$\frac{1}{4} {x}^{2}$ becomes $\frac{1}{4} \left(2 \cdot {x}^{2 - 1}\right)$, which in turn becomes $\frac{1}{2} x$.

Next, let's take the derivative of the second term, which is $- x$, and the derivative of a variable by itself is just 1. Taking into account the negative sign, this turns out to be $- 1$.

The last term is a constant, and the derivative of any constant is $0$, so that will replace the 4.

Combining all of our answers together, our final result is $\frac{1}{2} x - 1$.