Solve d^-3:d^-7

$$d ^ { - 3 } : d ^ { - 7 }$$

Differentiate w.r.t. d

$$4d^{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{1}{1}d^{-3-\left(-7\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}d}(d^{4})$$

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}.

$$4d^{4-1}$$

Do the arithmetic.

$$4d^{3}$$

Evaluate

$$d^{4}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -7 from -3 to get 4.

$$d^{4}$$