Solve (b^5)(b^6)(b)

$$( b ^ { 5 } ) ( b ^ { 6 } ) ( b )$$

Evaluate

$$b^{12}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$b^{5}b^{6}b^{1}$$

Use the Multiplication Rule for Exponents.

$$b^{5+6+1}$$

Add the exponents 5 and 6.

$$b^{11+1}$$

Add the exponents 11 and 1.

$$b^{12}$$

Differentiate w.r.t. b

$$12b^{11}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and 6 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}b}(b^{11}b)$$

To multiply powers of the same base, add their exponents. Add 11 and 1 to get 12.

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

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

$$12b^{12-1}$$

Subtract 1 from 12.

$$12b^{11}$$