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

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

Evaluate

$$6b^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$3b^{7}\times 2$$

Multiply 3 and 2 to get 6.

$$6b^{7}$$

Differentiate w.r.t. b

$$42b^{6}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}b}(3b^{7}\times 2)$$

Multiply 3 and 2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}b}(6b^{7})$$

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

$$7\times 6b^{7-1}$$

Multiply 7 times 6.

$$42b^{7-1}$$

Subtract 1 from 7.

$$42b^{6}$$