Solve 2xy^2/6x^3*y

$$\frac { 2 x y ^ { 2 } } { 6 x ^ { 3 } \cdot y }$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{2^{1}x^{1}y^{2}}{6^{1}x^{3}y^{1}}$$

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

$$\frac{2^{1}}{6^{1}}x^{1-3}y^{2-1}$$

Subtract 3 from 1.

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

Subtract 1 from 2.

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

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

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

Differentiate w.r.t. x

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2y^{2}}{6y}x^{1-3})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

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