Solve 60x^2y^3/12xy

$$\frac { 60 x ^ { 2 } y ^ { 3 } } { 12 x y }$$

Evaluate

$$5xy^{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{60^{1}x^{2}y^{3}}{12^{1}x^{1}y^{1}}$$

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

$$\frac{60^{1}}{12^{1}}x^{2-1}y^{3-1}$$

Subtract 1 from 2.

$$\frac{60^{1}}{12^{1}}x^{1}y^{3-1}$$

Subtract 1 from 3.

$$\frac{60^{1}}{12^{1}}xy^{2}$$

Divide 60 by 12.

$$5xy^{2}$$

Differentiate w.r.t. x

$$5y^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{60y^{3}}{12y}x^{2-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5y^{2}x^{1})$$

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}.

$$5y^{2}x^{1-1}$$

Do the arithmetic.

$$5y^{2}x^{0}$$

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

$$5y^{2}\times 1$$

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

$$5y^{2}$$