Solve 27b^418b^2

$$27 b ^ { 4 } 18 b ^ { 2 }$$

Evaluate

$$486b^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$27b^{6}\times 18$$

Multiply 27 and 18 to get 486.

$$486b^{6}$$

Differentiate w.r.t. b

$$2916b^{5}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}b}(27b^{6}\times 18)$$

Multiply 27 and 18 to get 486.

$$\frac{\mathrm{d}}{\mathrm{d}b}(486b^{6})$$

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

$$6\times 486b^{6-1}$$

Multiply 6 times 486.

$$2916b^{6-1}$$

Subtract 1 from 6.

$$2916b^{5}$$