Find the Derivative - d/dt (t^2)/2

Problem

d()/d(t)(t^2)/2

Solution

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

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

d()/d(t)(t^2)/2=1/2⋅d(t^2)/d(t)

3. Apply the power rule for derivatives, d(t^n)/d(t)=n*t^(n−1) where n=2

d(t^2)/d(t)=2*t^(2−1)

d(t^2)/d(t)=2*t

4. Multiply the constant factor by the derivative of the power term.

1/2⋅2*t=t

Final Answer

d()/d(t)(t^2)/2=t

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