Solve z^4/z^-1

$$\frac { z ^ { 4 } } { z ^ { - 1 } }$$

Differentiate w.r.t. z

$$5z^{4}$$

Solution Steps

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

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

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}z}(z^{5})$$

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}.

$$5z^{5-1}$$

Do the arithmetic.

$$5z^{4}$$

Evaluate

$$z^{5}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -1 from 4 to get 5.

$$z^{5}$$