Solve 1/a*(a/b)^frac{3{3}}

$$\frac { 1 } { a } \times ( \frac { a } { b } ) ^ { \frac { 3 } { 3 } }$$

Evaluate

$$\frac{1}{b}$$

Solution Steps

Divide 3 by 3 to get 1.

$$\frac{1}{a}\times \left(\frac{a}{b}\right)^{1}$$

Calculate \frac{a}{b} to the power of 1 and get \frac{a}{b}.

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

Multiply \frac{1}{a} times \frac{a}{b} by multiplying numerator times numerator and denominator times denominator.

$$\frac{a}{ab}$$

Cancel out a in both numerator and denominator.

$$\frac{1}{b}$$

Differentiate w.r.t. b

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

Steps Using Definition of a Derivative

Divide 3 by 3 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{1}{a}\times \left(\frac{a}{b}\right)^{1})$$

Calculate \frac{a}{b} to the power of 1 and get \frac{a}{b}.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{1}{a}\times \frac{a}{b})$$

Multiply \frac{1}{a} times \frac{a}{b} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{a}{ab})$$

Cancel out a in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{1}{b})$$

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

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

Subtract 1 from -1.

$$-b^{-2}$$