Solve -20x^3y^2/-5x^3y

$$\frac { - 20 x ^ { 3 } y ^ { 2 } } { - 5 x ^ { 3 } y }$$

Evaluate

$$4y$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{\left(-20\right)^{1}x^{3}y^{2}}{\left(-5\right)^{1}x^{3}y^{1}}$$

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

$$\frac{\left(-20\right)^{1}}{\left(-5\right)^{1}}x^{3-3}y^{2-1}$$

Subtract 3 from 3.

$$\frac{\left(-20\right)^{1}}{\left(-5\right)^{1}}x^{0}y^{2-1}$$

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

$$\frac{\left(-20\right)^{1}}{\left(-5\right)^{1}}y^{2-1}$$

Subtract 1 from 2.

$$\frac{\left(-20\right)^{1}}{\left(-5\right)^{1}}y^{1}$$

Divide -20 by -5.

$$4y$$

Differentiate w.r.t. y

$$4$$

Steps Using Definition of a Derivative

Cancel out 5yx^{3} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{-4y}{-1})$$

Anything divided by -1 gives its opposite.

$$\frac{\mathrm{d}}{\mathrm{d}y}(4y)$$

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

$$4y^{1-1}$$

Subtract 1 from 1.

$$4y^{0}$$

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

$$4\times 1$$

For any term t, t\times 1=t and 1t=t.

$$4$$