Solve 22y^6z^8/zyz^-7

$$\frac { 22 y ^ { 6 } z ^ { 8 } } { z y z ^ { - 7 } }$$

Evaluate

$$22y^{5}z^{14}$$

Solution Steps

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

$$\frac{22y^{6}z^{8}}{z^{-6}y}$$

Cancel out y in both numerator and denominator.

$$\frac{22y^{5}z^{8}}{z^{-6}}$$

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

$$22y^{5}z^{14}$$

Differentiate w.r.t. y

$$110y^{4}z^{14}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{22z^{8}z^{7}}{z}y^{6-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}y}(22z^{14}y^{5})$$

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}.

$$5\times 22z^{14}y^{5-1}$$

Do the arithmetic.

$$110z^{14}y^{4}$$