Solve 15x^2y^2/12x^3y

$$\frac { 15 x ^ { 2 } y ^ { 2 } } { 12 x ^ { 3 } y }$$

Evaluate

$$\frac{5y}{4x}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{15^{1}x^{2}y^{2}}{12^{1}x^{3}y^{1}}$$

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

$$\frac{15^{1}}{12^{1}}x^{2-3}y^{2-1}$$

Subtract 3 from 2.

$$\frac{15^{1}}{12^{1}}\times \frac{1}{x}y^{2-1}$$

Subtract 1 from 2.

$$\frac{15^{1}}{12^{1}}\times \frac{1}{x}y^{1}$$

Reduce the fraction \frac{15}{12} to lowest terms by extracting and canceling out 3.

$$\frac{5}{4}\times \frac{1}{x}y$$

Differentiate w.r.t. x

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{15y^{2}}{12y}x^{2-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5y}{4}\times \frac{1}{x})$$

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}.

$$-\frac{5y}{4}x^{-1-1}$$

Do the arithmetic.

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