Solve 14ab/7ab^2

$$\frac { 14 a b } { 7 a b ^ { 2 } }$$

Evaluate

$$\frac{2}{b}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{14^{1}a^{1}b^{1}}{7^{1}a^{1}b^{2}}$$

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

$$\frac{14^{1}}{7^{1}}a^{1-1}b^{1-2}$$

Subtract 1 from 1.

$$\frac{14^{1}}{7^{1}}a^{0}b^{1-2}$$

For any number a except 0, a^{0}=1.

$$\frac{14^{1}}{7^{1}}b^{1-2}$$

Subtract 2 from 1.

$$\frac{14^{1}}{7^{1}}\times \frac{1}{b}$$

Divide 14 by 7.

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

Differentiate w.r.t. b

$$-\frac{2}{b^{2}}$$

Steps Using Definition of a Derivative

Cancel out 7ab in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{2}{b})$$

The derivative of ax^{n} is nax^{n-1}.

$$-2b^{-1-1}$$

Subtract 1 from -1.

$$-2b^{-2}$$