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

Problem

d()/d(x)(x2)/2

Solution

1. Identify the constant factor in the expression. The expression (x2)/2 can be rewritten as 1/2⋅x2

2. Apply the constant multiple rule, which states that d()/d(x)*[c⋅ƒ(x)]=c⋅d(ƒ(x))/d(x)

d()/d(x)(x2)/2=1/2⋅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 derivative of the power function.

1/2⋅2*x=x

Final Answer

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

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