Solve p^-5/p^-4

$$\frac { p ^ { - 5 } } { p ^ { - 4 } }$$

Differentiate w.r.t. p

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}p}(\frac{1}{1}p^{-5-\left(-4\right)})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$-p^{-2}$$

Evaluate

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

Solution Steps

Rewrite p^{-4} as p^{-5}p. Cancel out p^{-5} in both numerator and denominator.

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