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

  1. Identify the function to differentiate

The function we have is ( f(x) = \frac{1}{4} x ).

  1. 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} ).

  1. Differentiate the variable

The derivative of ( x ) with respect to ( x ) is 1. So, we can express the derivative as: $$ f'(x) = \frac{1}{4} \cdot 1 $$

  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.
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