Solve 18xy^6/12x^3y^5

$$\frac { 18 x y ^ { 6 } } { 12 x ^ { 3 } y ^ { 5 } }$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{18^{1}x^{1}y^{6}}{12^{1}x^{3}y^{5}}$$

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

$$\frac{18^{1}}{12^{1}}x^{1-3}y^{6-5}$$

Subtract 3 from 1.

$$\frac{18^{1}}{12^{1}}x^{-2}y^{6-5}$$

Subtract 5 from 6.

$$\frac{18^{1}}{12^{1}}\times \frac{1}{x^{2}}y^{1}$$

Reduce the fraction \frac{18}{12} to lowest terms by extracting and canceling out 6.

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

Differentiate w.r.t. x

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{18y^{6}}{12y^{5}}x^{1-3})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

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