Solve (+12x^4y):(-6xy)=

$$( + 12 x ^ { 4 } y ) : ( - 6 x y ) =$$

Evaluate

$$-2x^{3}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{12^{1}x^{4}y^{1}}{\left(-6\right)^{1}x^{1}y^{1}}$$

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

$$\frac{12^{1}}{\left(-6\right)^{1}}x^{4-1}y^{1-1}$$

Subtract 1 from 4.

$$\frac{12^{1}}{\left(-6\right)^{1}}x^{3}y^{1-1}$$

Subtract 1 from 1.

$$\frac{12^{1}}{\left(-6\right)^{1}}x^{3}y^{0}$$

For any number a except 0, a^{0}=1.

$$\frac{12^{1}}{\left(-6\right)^{1}}x^{3}$$

Divide 12 by -6.

$$-2x^{3}$$

Differentiate w.r.t. x

$$-6x^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{12y}{-6y}x^{4-1})$$

Do the arithmetic.

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

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}.

$$3\left(-2\right)x^{3-1}$$

Do the arithmetic.

$$-6x^{2}$$