Solve 6x^3y/12x^2y

$$\frac { 6 x ^ { 3 } y } { 12 x ^ { 2 } y }$$

Evaluate

$$\frac{x}{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{6^{1}x^{3}y^{1}}{12^{1}x^{2}y^{1}}$$

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

$$\frac{6^{1}}{12^{1}}x^{3-2}y^{1-1}$$

Subtract 2 from 3.

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

Subtract 1 from 1.

$$\frac{6^{1}}{12^{1}}xy^{0}$$

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

$$\frac{6^{1}}{12^{1}}x$$

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

$$\frac{1}{2}x$$

Differentiate w.r.t. x

$$\frac{1}{2} = 0.5$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6y}{12y}x^{3-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{2}x^{1})$$

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}.

$$\frac{1}{2}x^{1-1}$$

Do the arithmetic.

$$\frac{1}{2}x^{0}$$

For any term t except 0, t^{0}=1.

$$\frac{1}{2}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{1}{2}$$