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Differentiate w.r.t. x
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\frac{\mathrm{d}}{\mathrm{d}x}(x+1)
Calculate x to the power of 0 and get 1.
x^{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}.
x^{0}
Subtract 1 from 1.
1
For any term t except 0, t^{0}=1.
x+1
Calculate x to the power of 0 and get 1.