What is the derivative of 1/4x?
Understand the Problem
The question is asking for the derivative of the function 1/4x with respect to x. To solve this, we'll apply the rules of differentiation.
Answer
The derivative is \( \frac{1}{4} \).
Answer for screen readers
The derivative of the function ( f(x) = \frac{1}{4} x ) with respect to ( x ) is ( \frac{1}{4} ).
Steps to Solve
- Identify the function to differentiate
The function we have is ( f(x) = \frac{1}{4} x ).
- Apply the constant multiple rule
When differentiating a constant multiplied by a variable, we apply the rule: ( f'(x) = c \cdot f'(x) ), where ( c ) is a constant. Here, ( c = \frac{1}{4} ).
- Differentiate the variable
The derivative of ( x ) with respect to ( x ) is 1. So, we can express the derivative as: $$ f'(x) = \frac{1}{4} \cdot 1 $$
- Simplify the derivative
Now we simplify the expression: $$ f'(x) = \frac{1}{4} $$
The derivative of the function ( f(x) = \frac{1}{4} x ) with respect to ( x ) is ( \frac{1}{4} ).
More Information
The result indicates that for every unit increase in ( x ), ( f(x) ) increases by ( \frac{1}{4} ). This represents a linear function with a constant slope.
Tips
- Forgetting the constant multiplier during differentiation. Always remember to apply the constant multiple rule correctly.
