Solve 6x^5y^3/3x^2y

$$\frac { 6 x ^ { 5 } y ^ { 3 } } { 3 x ^ { 2 } y }$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{6^{1}x^{5}y^{3}}{3^{1}x^{2}y^{1}}$$

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

$$\frac{6^{1}}{3^{1}}x^{5-2}y^{3-1}$$

Subtract 2 from 5.

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

Subtract 1 from 3.

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

Divide 6 by 3.

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

Differentiate w.r.t. x

$$6\left(xy\right)^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6y^{3}}{3y}x^{5-2})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$6y^{2}x^{2}$$