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Differentiate w.r.t. C_3
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5C_{3}^{1-1}
The derivative of ax^{n} is nax^{n-1}.
5C_{3}^{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.