Solve 3g^-7/3g^-7*g

$$\frac { 3 g ^ { - 7 } } { 3 g ^ { - 7 } \cdot g }$$

Evaluate

$$\frac{1}{g}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -7 and 1 to get -6.

$$\frac{3g^{-7}}{3g^{-6}}$$

Cancel out 3 in both numerator and denominator.

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

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

$$\frac{1}{g^{1}}$$

Calculate g to the power of 1 and get g.

$$\frac{1}{g}$$

Differentiate w.r.t. g

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{3}{3g}g^{-7-\left(-7\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{1}{g}g^{0})$$

For any number a except 0, a^{0}=1.

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

The derivative of a constant term is 0.

$$0$$