Solve (2)4b^3*2b^3

$$( 2 ) 4 b ^ { 3 } \cdot 2 b ^ { 3 }$$

Evaluate

$$16b^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$2\times 4b^{6}\times 2$$

Multiply 2 and 4 to get 8.

$$8b^{6}\times 2$$

Multiply 8 and 2 to get 16.

$$16b^{6}$$

Differentiate w.r.t. b

$$96b^{5}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}b}(2\times 4b^{6}\times 2)$$

Multiply 2 and 4 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}b}(8b^{6}\times 2)$$

Multiply 8 and 2 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}b}(16b^{6})$$

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

$$6\times 16b^{6-1}$$

Multiply 6 times 16.

$$96b^{6-1}$$

Subtract 1 from 6.

$$96b^{5}$$