Solve d^-2/d^-18

$$\frac { d ^ { - 2 } } { d ^ { - 18 } }$$

Differentiate w.r.t. d

$$16d^{15}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{1}{1}d^{-2-\left(-18\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}d}(d^{16})$$

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}.

$$16d^{16-1}$$

Do the arithmetic.

$$16d^{15}$$

Evaluate

$$d^{16}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -18 from -2 to get 16.

$$d^{16}$$