Solve 75x^3y^2/30xy

$$\frac { 75 x ^ { 3 } y ^ { 2 } } { 30 x y }$$

Evaluate

$$\frac{5yx^{2}}{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{75^{1}x^{3}y^{2}}{30^{1}x^{1}y^{1}}$$

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

$$\frac{75^{1}}{30^{1}}x^{3-1}y^{2-1}$$

Subtract 1 from 3.

$$\frac{75^{1}}{30^{1}}x^{2}y^{2-1}$$

Subtract 1 from 2.

$$\frac{75^{1}}{30^{1}}x^{2}y^{1}$$

Reduce the fraction \frac{75}{30} to lowest terms by extracting and canceling out 15.

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

Differentiate w.r.t. x

$$5xy$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{75y^{2}}{30y}x^{3-1})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$5yx^{1}$$

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

$$5yx$$