Solve 2q^-7/2q^0*q^-1

$$\frac { 2 q ^ { - 7 } } { 2 q ^ { 0 } \cdot q ^ { - 1 } }$$

Evaluate

$$\frac{1}{q^{6}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 0 and -1 to get -1.

$$\frac{2q^{-7}}{2q^{-1}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{q^{-7}}{\frac{1}{q}}$$

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

$$\frac{1}{q^{6}}$$

Differentiate w.r.t. q

$$-\frac{6}{q^{7}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}q}(\frac{2}{2q^{0}}q^{-7-\left(-1\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}q}(q^{-6})$$

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}.

$$-6q^{-6-1}$$

Do the arithmetic.

$$-6q^{-7}$$