Solve 2b^5quad5quad17b^6

$$2 b ^ { 5 } \quad 5 \quad 17 b ^ { 6 }$$

Evaluate

$$170b^{11}$$

Solution Steps

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

$$2b^{11}\times 5\times 17$$

Multiply 2 and 5 to get 10.

$$10b^{11}\times 17$$

Multiply 10 and 17 to get 170.

$$170b^{11}$$

Differentiate w.r.t. b

$$1870b^{10}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}b}(2b^{11}\times 5\times 17)$$

Multiply 2 and 5 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}b}(10b^{11}\times 17)$$

Multiply 10 and 17 to get 170.

$$\frac{\mathrm{d}}{\mathrm{d}b}(170b^{11})$$

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

$$11\times 170b^{11-1}$$

Multiply 11 times 170.

$$1870b^{11-1}$$

Subtract 1 from 11.

$$1870b^{10}$$