Solve 7x^2y^5/14xy^4

$$\frac { 7 x ^ { 2 } y ^ { 5 } } { 14 x y ^ { 4 } }$$

Evaluate

$$\frac{xy}{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{7^{1}x^{2}y^{5}}{14^{1}x^{1}y^{4}}$$

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

$$\frac{7^{1}}{14^{1}}x^{2-1}y^{5-4}$$

Subtract 1 from 2.

$$\frac{7^{1}}{14^{1}}x^{1}y^{5-4}$$

Subtract 4 from 5.

$$\frac{7^{1}}{14^{1}}xy^{1}$$

Reduce the fraction \frac{7}{14} to lowest terms by extracting and canceling out 7.

$$\frac{1}{2}xy$$

Differentiate w.r.t. x

$$\frac{y}{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7y^{5}}{14y^{4}}x^{2-1})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$\frac{y}{2}x^{0}$$

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

$$\frac{y}{2}\times 1$$

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

$$\frac{y}{2}$$