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

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.

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.

By signing up, you agree to our Terms of Service and Privacy Policy

To find the derivative of ( f(x) = \frac{1}{4}x^2 - x + 4 ), you can apply the power rule and the constant rule. The derivative of ( x^n ) is ( nx^{n-1} ), and the derivative of a constant is 0.

So, for ( f(x) = \frac{1}{4}x^2 - x + 4 ):

- The derivative of ( \frac{1}{4}x^2 ) is ( \frac{1}{4} \times 2x = \frac{1}{2}x ).
- The derivative of ( -x ) is ( -1 ).
- The derivative of the constant term 4 is 0.

Therefore, the derivative of ( f(x) = \frac{1}{4}x^2 - x + 4 ) is ( f'(x) = \frac{1}{2}x - 1 ).

By signing up, you agree to our Terms of Service and Privacy Policy

To find the derivative of the function ( f(x) = \frac{1}{4}x^2 - x + 4 ), we can apply the power rule and the constant multiple rule of differentiation:

- For ( \frac{1}{4}x^2 ), using the power rule, the derivative is ( \frac{1}{4} \cdot 2x = \frac{1}{2}x ).
- For ( -x ), the derivative of a constant multiple of x is simply the constant itself. So, the derivative of ( -x ) is ( -1 ).
- For the constant term 4, the derivative of a constant is zero.

Combining these results, the derivative of the function ( f(x) = \frac{1}{4}x^2 - x + 4 ) is:

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

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7