D^2-2DD'+D'^2

asked by guest
on Nov 24, 2024 at 12:17 am



You asked:

Evaluate the expression: \({D}^{2} - 2 D \cdot D^{\prime} + {D^{\prime}}^{2}\)

MathBot Answer:

Evaluated



\(\displaystyle {D}^{2} - 2 D \cdot D^{\prime} + {D^{\prime}}^{2} = D^{2}{\left(t \right)} - 2 D{\left(t \right)} \frac{d}{d t} D{\left(t \right)} + \left(\frac{d}{d t} D{\left(t \right)}\right)^{2} \)

Factored

\[{D}^{2} - 2 D \cdot D^{\prime} + {D^{\prime}}^{2} = \left(D{\left(t \right)} - \frac{d}{d t} D{\left(t \right)}\right)^{2}\]

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