Solve 2b*2b*2b*2b*2b

$$2 b \cdot 2 b \cdot 2 b \cdot 2 b \cdot 2 b$$

Evaluate

$$32b^{5}$$

Solution Steps

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

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

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

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

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

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

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$2b^{5}\times 2\times 2\times 2\times 2$$

Multiply 2 and 2 to get 4.

$$4b^{5}\times 2\times 2\times 2$$

Multiply 4 and 2 to get 8.

$$8b^{5}\times 2\times 2$$

Multiply 8 and 2 to get 16.

$$16b^{5}\times 2$$

Multiply 16 and 2 to get 32.

$$32b^{5}$$

Differentiate w.r.t. b

$$160b^{4}$$

Steps Using Definition of a Derivative

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

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

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

$$\frac{\mathrm{d}}{\mathrm{d}b}(2b^{3}\times 2\times 2\times 2b\times 2b)$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

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

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}b}(2b^{5}\times 2\times 2\times 2\times 2)$$

Multiply 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}b}(4b^{5}\times 2\times 2\times 2)$$

Multiply 4 and 2 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}b}(8b^{5}\times 2\times 2)$$

Multiply 8 and 2 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}b}(16b^{5}\times 2)$$

Multiply 16 and 2 to get 32.

$$\frac{\mathrm{d}}{\mathrm{d}b}(32b^{5})$$

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

$$5\times 32b^{5-1}$$

Multiply 5 times 32.

$$160b^{5-1}$$

Subtract 1 from 5.

$$160b^{4}$$