Solve (-1/48x^3y^2)div(1/16x^2y)

$$( - \frac { 1 } { 48 } x ^ { 3 } y ^ { 2 } ) \div ( \frac { 1 } { 16 } x ^ { 2 } y )$$

Evaluate

$$-\frac{xy}{3}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{\left(-\frac{1}{48}\right)^{1}x^{3}y^{2}}{\left(\frac{1}{16}\right)^{1}x^{2}y^{1}}$$

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

$$\frac{\left(-\frac{1}{48}\right)^{1}}{\left(\frac{1}{16}\right)^{1}}x^{3-2}y^{2-1}$$

Subtract 2 from 3.

$$\frac{\left(-\frac{1}{48}\right)^{1}}{\left(\frac{1}{16}\right)^{1}}x^{1}y^{2-1}$$

Subtract 1 from 2.

$$\frac{\left(-\frac{1}{48}\right)^{1}}{\left(\frac{1}{16}\right)^{1}}xy^{1}$$

Divide -\frac{1}{48} by \frac{1}{16} by multiplying -\frac{1}{48} by the reciprocal of \frac{1}{16}.

$$-\frac{1}{3}xy$$

Differentiate w.r.t. x

$$-\frac{y}{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{16\left(-\frac{y^{2}}{48}\right)}{y}x^{3-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{y}{3}\right)x^{1})$$

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}.

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

Do the arithmetic.

$$\left(-\frac{y}{3}\right)x^{0}$$

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

$$\left(-\frac{y}{3}\right)\times 1$$

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

$$-\frac{y}{3}$$