Solve g^9/g^-4

$$\frac { g ^ { 9 } } { g ^ { - 4 } }$$

Differentiate w.r.t. g

$$13g^{12}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{1}{1}g^{9-\left(-4\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}g}(g^{13})$$

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}.

$$13g^{13-1}$$

Do the arithmetic.

$$13g^{12}$$

Evaluate

$$g^{13}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -4 from 9 to get 13.

$$g^{13}$$