Solve -24x^2y^5/-18x^4y^4

$$\frac { - 24 x ^ { 2 } y ^ { 5 } } { - 18 x ^ { 4 } y ^ { 4 } }$$

Evaluate

$$\frac{4y}{3x^{2}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{\left(-24\right)^{1}x^{2}y^{5}}{\left(-18\right)^{1}x^{4}y^{4}}$$

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

$$\frac{\left(-24\right)^{1}}{\left(-18\right)^{1}}x^{2-4}y^{5-4}$$

Subtract 4 from 2.

$$\frac{\left(-24\right)^{1}}{\left(-18\right)^{1}}x^{-2}y^{5-4}$$

Subtract 4 from 5.

$$\frac{\left(-24\right)^{1}}{\left(-18\right)^{1}}\times \frac{1}{x^{2}}y^{1}$$

Reduce the fraction \frac{-24}{-18} to lowest terms by extracting and canceling out 6.

$$\frac{4}{3}\times \frac{1}{x^{2}}y$$

Differentiate w.r.t. x

$$-\frac{8y}{3x^{3}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{24y^{5}}{-18y^{4}}\right)x^{2-4})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4y}{3}x^{-2})$$

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}.

$$-2\times \frac{4y}{3}x^{-2-1}$$

Do the arithmetic.

$$\left(-\frac{8y}{3}\right)x^{-3}$$