Solve q^-2/q^-3

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

Evaluate

$$q$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -3 from -2 to get 1.

$$q^{1}$$

Calculate q to the power of 1 and get q.

$$q$$

Differentiate w.r.t. q

$$1$$

Solution Steps

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

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

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}q}(q^{1})$$

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}.

$$q^{1-1}$$

Do the arithmetic.

$$q^{0}$$

For any term t except 0, t^{0}=1.

$$1$$