Solve xy^2/xy

$$\frac { x y ^ { 2 } } { x y }$$

Evaluate

$$y$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{x^{1}y^{2}}{x^{1}y^{1}}$$

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

$$x^{1-1}y^{2-1}$$

Subtract 1 from 1.

$$x^{0}y^{2-1}$$

Subtract 1 from 2.

$$x^{0}y^{1}$$

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

$$y$$

Differentiate w.r.t. y

$$1$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{x}{x}y^{2-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{1})$$

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}.

$$y^{1-1}$$

Do the arithmetic.

$$y^{0}$$

For any term t except 0, t^{0}=1.

$$1$$