Solve v/20!

$$\frac { v } { 20 ! }$$

Differentiate w.r.t. v

$$\frac{1}{2432902008176640000} = 4.110317623312165 \times 10^{-19}$$

Steps Using Definition of a Derivative

The factorial of 20 is 2432902008176640000.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{v}{2432902008176640000})$$

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

$$\frac{1}{2432902008176640000}v^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{2432902008176640000}v^{0}$$

For any term t except 0, t^{0}=1.

$$\frac{1}{2432902008176640000}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{1}{2432902008176640000}$$

Evaluate

$$\frac{v}{2432902008176640000}$$

Solution Steps

The factorial of 20 is 2432902008176640000.

$$\frac{v}{2432902008176640000}$$