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Differentiate w.r.t. x
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2x^{2-1}-5x^{1-1}
The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.
2x^{1}-5x^{1-1}
Subtract 1 from 2.
2x^{1}-5x^{0}
Subtract 1 from 1.
2x-5x^{0}
For any term t, t^{1}=t.
2x-5
For any term t except 0, t^{0}=1.
x^{2}-5x+13
Divide 117 by 9 to get 13.