Solve z^14/z^-15

$$\frac { z ^ { 14 } } { z ^ { - 15 } }$$

Differentiate w.r.t. z

$$29z^{28}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}z}(\frac{1}{1}z^{14-\left(-15\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}z}(z^{29})$$

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}.

$$29z^{29-1}$$

Do the arithmetic.

$$29z^{28}$$

Evaluate

$$z^{29}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -15 from 14 to get 29.

$$z^{29}$$