Solve (+6xy^2)div(-3xy)

$$(+6x { y }^{ 2 } ) \div (-3xy)$$

Evaluate

$$-2y$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{6^{1}x^{1}y^{2}}{\left(-3\right)^{1}x^{1}y^{1}}$$

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

$$\frac{6^{1}}{\left(-3\right)^{1}}x^{1-1}y^{2-1}$$

Subtract 1 from 1.

$$\frac{6^{1}}{\left(-3\right)^{1}}x^{0}y^{2-1}$$

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

$$\frac{6^{1}}{\left(-3\right)^{1}}y^{2-1}$$

Subtract 1 from 2.

$$\frac{6^{1}}{\left(-3\right)^{1}}y^{1}$$

Divide 6 by -3.

$$-2y$$

Differentiate w.r.t. y

$$-2$$

Steps Using Definition of a Derivative

Cancel out 3xy in both numerator and denominator.

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

Anything divided by -1 gives its opposite.

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

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

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

Subtract 1 from 1.

$$-2y^{0}$$

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

$$-2$$