Solve 8x^3y/4x^2y^2

$$\frac{ 8 { x }^{ 3 } y }{ 4 { x }^{ 2 } { y }^{ 2 } }$$

Evaluate

$$\frac{2x}{y}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{8^{1}x^{3}y^{1}}{4^{1}x^{2}y^{2}}$$

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

$$\frac{8^{1}}{4^{1}}x^{3-2}y^{1-2}$$

Subtract 2 from 3.

$$\frac{8^{1}}{4^{1}}x^{1}y^{1-2}$$

Subtract 2 from 1.

$$\frac{8^{1}}{4^{1}}x\times \frac{1}{y}$$

Divide 8 by 4.

$$2x\times \frac{1}{y}$$

Differentiate w.r.t. x

$$\frac{2}{y}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8y}{4y^{2}}x^{3-2})$$

Do the arithmetic.

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

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

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

Do the arithmetic.

$$\frac{2}{y}x^{0}$$

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

$$\frac{2}{y}\times 1$$

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

$$\frac{2}{y}$$