Solve 6xy^2/4x^2y=

$$\frac { 6 x y ^ { 2 } } { 4 x ^ { 2 } y } =$$

Evaluate

$$\frac{3y}{2x}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{6^{1}x^{1}y^{2}}{4^{1}x^{2}y^{1}}$$

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

$$\frac{6^{1}}{4^{1}}x^{1-2}y^{2-1}$$

Subtract 2 from 1.

$$\frac{6^{1}}{4^{1}}\times \frac{1}{x}y^{2-1}$$

Subtract 1 from 2.

$$\frac{6^{1}}{4^{1}}\times \frac{1}{x}y^{1}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{3}{2}\times \frac{1}{x}y$$

Differentiate w.r.t. x

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6y^{2}}{4y}x^{1-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3y}{2}\times \frac{1}{x})$$

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}.

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

Do the arithmetic.

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