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

1 Answer
Dec 17, 2017

#1/2x-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 #nx^(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.

#1/4x^2# becomes #1/4(2*x^(2-1))#, which in turn becomes #1/2x#.

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 #1/2x-1#.