Solve 15xy^5/5xy^2

$$\frac { 15 x y ^ { 5 } } { 5 x y ^ { 2 } }$$

Evaluate

$$3y^{3}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{15^{1}x^{1}y^{5}}{5^{1}x^{1}y^{2}}$$

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

$$\frac{15^{1}}{5^{1}}x^{1-1}y^{5-2}$$

Subtract 1 from 1.

$$\frac{15^{1}}{5^{1}}x^{0}y^{5-2}$$

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

$$\frac{15^{1}}{5^{1}}y^{5-2}$$

Subtract 2 from 5.

$$\frac{15^{1}}{5^{1}}y^{3}$$

Divide 15 by 5.

$$3y^{3}$$

Differentiate w.r.t. y

$$9y^{2}$$

Steps Using Definition of a Derivative

Cancel out 5xy^{2} in both numerator and denominator.

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

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

$$3\times 3y^{3-1}$$

Multiply 3 times 3.

$$9y^{3-1}$$

Subtract 1 from 3.

$$9y^{2}$$