Solve 15x^4y^2/3xy

$$\frac { 15 x ^ { 4 } y ^ { 2 } } { 3 x y }$$

Evaluate

$$5yx^{3}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{15^{1}x^{4}y^{2}}{3^{1}x^{1}y^{1}}$$

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

$$\frac{15^{1}}{3^{1}}x^{4-1}y^{2-1}$$

Subtract 1 from 4.

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

Subtract 1 from 2.

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

Divide 15 by 3.

$$5x^{3}y$$

Differentiate w.r.t. x

$$15yx^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{15y^{2}}{3y}x^{4-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5yx^{3})$$

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}.

$$3\times 5yx^{3-1}$$

Do the arithmetic.

$$15yx^{2}$$