Solve 20b^22*14^18

$$20 b ^ { 22 } \times 14 ^ { 18 }$$

Evaluate

$$8537577084212734853120b^{22}$$

Solution Steps

Calculate 14 to the power of 18 and get 426878854210636742656.

$$20b^{22}\times 426878854210636742656$$

Multiply 20 and 426878854210636742656 to get 8537577084212734853120.

$$8537577084212734853120b^{22}$$

Differentiate w.r.t. b

$$187826695852680166768640b^{21}$$

Steps Using Definition of a Derivative

Calculate 14 to the power of 18 and get 426878854210636742656.

$$\frac{\mathrm{d}}{\mathrm{d}b}(20b^{22}\times 426878854210636742656)$$

Multiply 20 and 426878854210636742656 to get 8537577084212734853120.

$$\frac{\mathrm{d}}{\mathrm{d}b}(8537577084212734853120b^{22})$$

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

$$22\times 8537577084212734853120b^{22-1}$$

Multiply 22 times 8537577084212734853120.

$$187826695852680166768640b^{22-1}$$

Subtract 1 from 22.

$$187826695852680166768640b^{21}$$