Solve d^3/d^8

$$\frac { d ^ { 3 } } { d ^ { 8 } }$$

Evaluate

$$\frac{1}{d^{5}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{d^{3}}{d^{8}}$$

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

$$d^{3-8}$$

Subtract 8 from 3.

$$d^{-5}$$

Differentiate w.r.t. d

$$-\frac{5}{d^{6}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{1}{1}d^{3-8})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}d}(d^{-5})$$

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}.

$$-5d^{-5-1}$$

Do the arithmetic.

$$-5d^{-6}$$