Solve t^-3/t^-2

$$\frac { t ^ { - 3 } } { t ^ { - 2 } }$$

Differentiate w.r.t. t

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}t}(\frac{1}{1}t^{-3-\left(-2\right)})$$

Do the arithmetic.

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

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}.

$$-t^{-1-1}$$

Do the arithmetic.

$$-t^{-2}$$

Evaluate

$$\frac{1}{t}$$

Solution Steps

Rewrite t^{-2} as t^{-3}t. Cancel out t^{-3} in both numerator and denominator.

$$\frac{1}{t}$$