Solve 7x^3y:(-14/3xy)

$$7 x ^ { 3 } y : ( - \frac { 14 } { 3 } x y )$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{7^{1}x^{3}y^{1}}{\left(-\frac{14}{3}\right)^{1}x^{1}y^{1}}$$

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

$$\frac{7^{1}}{\left(-\frac{14}{3}\right)^{1}}x^{3-1}y^{1-1}$$

Subtract 1 from 3.

$$\frac{7^{1}}{\left(-\frac{14}{3}\right)^{1}}x^{2}y^{1-1}$$

Subtract 1 from 1.

$$\frac{7^{1}}{\left(-\frac{14}{3}\right)^{1}}x^{2}y^{0}$$

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

$$\frac{7^{1}}{\left(-\frac{14}{3}\right)^{1}}x^{2}$$

Divide 7 by -\frac{14}{3} by multiplying 7 by the reciprocal of -\frac{14}{3}.

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

Differentiate w.r.t. x

$$-3x$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7y}{-\frac{14y}{3}}x^{3-1})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$-3x^{1}$$

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

$$-3x$$