Solve x^5y^2/xy^2

$$\frac { x ^ { 5 } y ^ { 2 } } { x y ^ { 2 } }$$

Evaluate

$$x^{4}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{x^{5}y^{2}}{x^{1}y^{2}}$$

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

$$x^{5-1}y^{2-2}$$

Subtract 1 from 5.

$$x^{4}y^{2-2}$$

Subtract 2 from 2.

$$x^{4}y^{0}$$

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

$$x^{4}$$

Differentiate w.r.t. x

$$4x^{3}$$

Steps Using Definition of a Derivative

Cancel out xy^{2} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{4})$$

The derivative of ax^{n} is nax^{n-1}.

$$4x^{4-1}$$

Subtract 1 from 4.

$$4x^{3}$$