Solve 6x^4y^3/12xy

$$\frac { 6 x ^ { 4 } y ^ { 3 } } { 12 x y }$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{6^{1}x^{4}y^{3}}{12^{1}x^{1}y^{1}}$$

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

$$\frac{6^{1}}{12^{1}}x^{4-1}y^{3-1}$$

Subtract 1 from 4.

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

Subtract 1 from 3.

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

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

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

Differentiate w.r.t. x

$$\frac{3\left(xy\right)^{2}}{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6y^{3}}{12y}x^{4-1})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

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