Solve 5!x

$$5 ! x$$

Differentiate w.r.t. x

$$120$$

Steps Using Definition of a Derivative

The factorial of 5 is 120.

$$\frac{\mathrm{d}}{\mathrm{d}x}(120x)$$

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

$$120x^{1-1}$$

Subtract 1 from 1.

$$120x^{0}$$

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

$$120\times 1$$

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

$$120$$

Evaluate

$$120x$$

Solution Steps

The factorial of 5 is 120.

$$120x$$