Solve (7b^3)(2b)=

$$( 7 b ^ { 3 } ) ( 2 b ) =$$

Evaluate

$$14b^{4}$$

Solution Steps

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

$$7b^{4}\times 2$$

Multiply 7 and 2 to get 14.

$$14b^{4}$$

Differentiate w.r.t. b

$$56b^{3}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}b}(7b^{4}\times 2)$$

Multiply 7 and 2 to get 14.

$$\frac{\mathrm{d}}{\mathrm{d}b}(14b^{4})$$

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

$$4\times 14b^{4-1}$$

Multiply 4 times 14.

$$56b^{4-1}$$

Subtract 1 from 4.

$$56b^{3}$$