Find the Derivative - d/dx (x^2)/4

Problem

d()/d(x)(x2)/4

Solution

1. Identify the constant factor in the expression. The expression (x2)/4 can be rewritten as 1/4⋅x2

2. Apply the constant multiple rule, which states that the derivative of a constant times a function is the constant times the derivative of the function.

d()/d(x)(x2)/4=1/4⋅d(x2)/d(x)

3. Apply the power rule to differentiate x2 The power rule states that d(xn)/d(x)=n*x(n−1)

d(x2)/d(x)=2*x

4. Multiply the constant factor by the result of the derivative.

1/4⋅2*x=(2*x)/4

5. Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 2

(2*x)/4=x/2

Final Answer

d()/d(x)(x2)/4=x/2

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