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Differentiate w.r.t. x_0
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5x_{0}^{1-1}
The derivative of ax^{n} is nax^{n-1}.
5x_{0}^{0}
Subtract 1 from 1.
5\times 1
For any term t except 0, t^{0}=1.
5
For any term t, t\times 1=t and 1t=t.