Solve x^3y/xy

$$\frac { x ^ { 3 } y } { x y }$$

Evaluate

$$x^{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{x^{3}y^{1}}{x^{1}y^{1}}$$

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

$$x^{3-1}y^{1-1}$$

Subtract 1 from 3.

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

Subtract 1 from 1.

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

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

$$x^{2}$$

Differentiate w.r.t. x

$$2x$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{y}{y}x^{3-1})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$2x^{1}$$

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

$$2x$$