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Differentiate w.r.t. x
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\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-1)
Cancel out ∂ in both numerator and denominator.
2x^{2-1}
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}
Subtract 1 from 2.
2x
For any term t, t^{1}=t.
x^{2}-1
Cancel out ∂ in both numerator and denominator.