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Differentiate w.r.t. d
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\frac{\mathrm{d}}{\mathrm{d}d}(\frac{1}{1}d^{-2-\left(-18\right)})
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.
\frac{\mathrm{d}}{\mathrm{d}d}(d^{16})
Do the arithmetic.
16d^{16-1}
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}.
16d^{15}
Do the arithmetic.
d^{16}
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -18 from -2 to get 16.