Solve b*b*b/12

$$\frac { b \times b \times b } { 12 }$$

Evaluate

$$\frac{b^{3}}{12}$$

Solution Steps

Multiply b and b to get b^{2}.

$$\frac{b^{2}b}{12}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{b^{3}}{12}$$

Differentiate w.r.t. b

$$\frac{b^{2}}{4}$$

Steps Using Definition of a Derivative

Multiply b and b to get b^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{b^{2}b}{12})$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{b^{3}}{12})$$

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

$$3\times \frac{1}{12}b^{3-1}$$

Multiply 3 times \frac{1}{12}.

$$\frac{1}{4}b^{3-1}$$

Subtract 1 from 3.

$$\frac{1}{4}b^{2}$$