Solve (-3/5x^2y^3)div(3x^2y)

$$( - \frac { 3 } { 5 } x ^ { 2 } y ^ { 3 } ) \div ( 3 x ^ { 2 } y )$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{\left(-\frac{3}{5}\right)^{1}x^{2}y^{3}}{3^{1}x^{2}y^{1}}$$

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

$$\frac{\left(-\frac{3}{5}\right)^{1}}{3^{1}}x^{2-2}y^{3-1}$$

Subtract 2 from 2.

$$\frac{\left(-\frac{3}{5}\right)^{1}}{3^{1}}x^{0}y^{3-1}$$

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

$$\frac{\left(-\frac{3}{5}\right)^{1}}{3^{1}}y^{3-1}$$

Subtract 1 from 3.

$$\frac{\left(-\frac{3}{5}\right)^{1}}{3^{1}}y^{2}$$

Divide -\frac{3}{5} by 3.

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

Differentiate w.r.t. y

$$-\frac{2y}{5}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{-\frac{3}{5}y^{2}}{3})$$

Divide -\frac{3}{5}y^{2} by 3 to get -\frac{1}{5}y^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-\frac{1}{5}y^{2})$$

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

$$2\left(-\frac{1}{5}\right)y^{2-1}$$

Multiply 2 times -\frac{1}{5}.

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

Subtract 1 from 2.

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

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

$$-\frac{2}{5}y$$