Solve d(t^3/-2t)/dt

$$\frac { d ( \frac { t ^ { 3 } } { - 2 t } ) } { d t }$$

Evaluate

$$-t$$

Solution Steps

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

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

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$-t^{1}$$

For any term t, t^{1}=t.

$$-t$$

Differentiate w.r.t. t

$$-1$$