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

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

Evaluate

$$-4y^{4}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

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

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

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

Subtract 3 from 3.

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

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

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

Subtract 1 from 5.

$$\frac{20^{1}}{\left(-5\right)^{1}}y^{4}$$

Divide 20 by -5.

$$-4y^{4}$$

Differentiate w.r.t. y

$$-16y^{3}$$

Steps Using Definition of a Derivative

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

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

Anything divided by -1 gives its opposite.

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

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

$$4\left(-4\right)y^{4-1}$$

Multiply 4 times -4.

$$-16y^{4-1}$$

Subtract 1 from 4.

$$-16y^{3}$$