Solve (-14x^7y^5):(+7x^5y^2)

$$( - 14 x ^ { 7 } y ^ { 5 } ) : ( + 7 x ^ { 5 } y ^ { 2 } )$$

Evaluate

$$-2x^{2}y^{3}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{\left(-14\right)^{1}x^{7}y^{5}}{7^{1}x^{5}y^{2}}$$

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

$$\frac{\left(-14\right)^{1}}{7^{1}}x^{7-5}y^{5-2}$$

Subtract 5 from 7.

$$\frac{\left(-14\right)^{1}}{7^{1}}x^{2}y^{5-2}$$

Subtract 2 from 5.

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

Divide -14 by 7.

$$-2x^{2}y^{3}$$

Differentiate w.r.t. x

$$-4xy^{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{14y^{5}}{7y^{2}}\right)x^{7-5})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$\left(-4y^{3}\right)x^{1}$$

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

$$\left(-4y^{3}\right)x$$