Solve t/t/2t

$$\frac { \frac { t } { t } } { 2 t }$$

Differentiate w.r.t. t

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

Solution Steps

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

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

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}t}(\frac{t}{2}t^{-2})$$

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}.

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

Do the arithmetic.

$$\left(-t\right)t^{-3}$$

Evaluate

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

Solution Steps

Divide t by t to get 1.

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