Solve p^0/p

$$\frac { p ^ { 0 } } { p }$$

Evaluate

$$\frac{1}{p}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{p^{0}}{p^{1}}$$

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

$$p^{-1}$$

Subtract 1 from 0.

$$\frac{1}{p}$$

Differentiate w.r.t. p

$$-\frac{1}{p^{2}}$$

Steps Using Definition of a Derivative

Rewrite p as p^{0}p. Cancel out p^{0} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}p}(\frac{1}{p})$$

The derivative of ax^{n} is nax^{n-1}.

$$-p^{-1-1}$$

Subtract 1 from -1.

$$-p^{-2}$$