Solve (-6x^3y)div(-3xy)

$$(-6 { x }^{ 3 } y) \div (-3xy)$$

Evaluate

$$2x^{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

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

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

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

Subtract 1 from 3.

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

Subtract 1 from 1.

$$\frac{\left(-6\right)^{1}}{\left(-3\right)^{1}}x^{2}y^{0}$$

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

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

Divide -6 by -3.

$$2x^{2}$$

Differentiate w.r.t. x

$$4x$$

Solution Steps

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

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

Do the arithmetic.

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

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}.

$$2\times 2x^{2-1}$$

Do the arithmetic.

$$4x^{1}$$

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

$$4x$$