Solve 21x^3y/14x^2y^2

$$\frac { 21 x ^ { 3 } y } { 14 x ^ { 2 } y ^ { 2 } }$$

Evaluate

$$\frac{3x}{2y}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{21^{1}x^{3}y^{1}}{14^{1}x^{2}y^{2}}$$

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

$$\frac{21^{1}}{14^{1}}x^{3-2}y^{1-2}$$

Subtract 2 from 3.

$$\frac{21^{1}}{14^{1}}x^{1}y^{1-2}$$

Subtract 2 from 1.

$$\frac{21^{1}}{14^{1}}x\times \frac{1}{y}$$

Reduce the fraction \frac{21}{14} to lowest terms by extracting and canceling out 7.

$$\frac{3}{2}x\times \frac{1}{y}$$

Differentiate w.r.t. x

$$\frac{3}{2y}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{21y}{14y^{2}}x^{3-2})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$\frac{3}{2y}x^{0}$$

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

$$\frac{3}{2y}\times 1$$

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

$$\frac{3}{2y}$$