Solve b^2/b^3*b^3

$$\frac { b ^ { 2 } } { b ^ { 3 } } \times b ^ { 3 }$$

Evaluate

$$b^{2}$$

Solution Steps

Rewrite b^{3} as b^{2}b. Cancel out b^{2} in both numerator and denominator.

$$\frac{1}{b}b^{3}$$

Express \frac{1}{b}b^{3} as a single fraction.

$$\frac{b^{3}}{b}$$

Cancel out b in both numerator and denominator.

$$b^{2}$$

Differentiate w.r.t. b

$$2b$$

Steps Using Definition of a Derivative

Rewrite b^{3} as b^{2}b. Cancel out b^{2} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{1}{b}b^{3})$$

Express \frac{1}{b}b^{3} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{b^{3}}{b})$$

Cancel out b in both numerator and denominator.

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

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

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

Subtract 1 from 2.

$$2b^{1}$$

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

$$2b$$