Solve -18x^3y^2/6x^2y=

$$\frac { - 18 x ^ { 3 } y ^ { 2 } } { 6 x ^ { 2 } y } =$$

Evaluate

$$-3xy$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{\left(-18\right)^{1}x^{3}y^{2}}{6^{1}x^{2}y^{1}}$$

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

$$\frac{\left(-18\right)^{1}}{6^{1}}x^{3-2}y^{2-1}$$

Subtract 2 from 3.

$$\frac{\left(-18\right)^{1}}{6^{1}}x^{1}y^{2-1}$$

Subtract 1 from 2.

$$\frac{\left(-18\right)^{1}}{6^{1}}xy^{1}$$

Divide -18 by 6.

$$-3xy$$

Differentiate w.r.t. x

$$-3y$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{18y^{2}}{6y}\right)x^{3-2})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

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

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

$$\left(-3y\right)\times 1$$

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

$$-3y$$