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Differentiate w.r.t. x
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\frac{\mathrm{d}}{\mathrm{d}x}(12x-1)
Multiply 3 and 4 to get 12.
12x^{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}.
12x^{0}
Subtract 1 from 1.
12\times 1
For any term t except 0, t^{0}=1.
12
For any term t, t\times 1=t and 1t=t.
12x-1
Multiply 3 and 4 to get 12.