Solve 2b^5*3b^2*b

$$2 b ^ { 5 } \times 3 b ^ { 2 } \times b$$

Evaluate

$$6b^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

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

To multiply powers of the same base, add their exponents. Add 7 and 1 to get 8.

$$2b^{8}\times 3$$

Multiply 2 and 3 to get 6.

$$6b^{8}$$

Differentiate w.r.t. b

$$48b^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

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

To multiply powers of the same base, add their exponents. Add 7 and 1 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}b}(2b^{8}\times 3)$$

Multiply 2 and 3 to get 6.

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

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

$$8\times 6b^{8-1}$$

Multiply 8 times 6.

$$48b^{8-1}$$

Subtract 1 from 8.

$$48b^{7}$$