Solve 2varepsilon/1!(1

$$\frac { 2 \varepsilon } { 1 ! } ( 1$$

Evaluate

$$2\epsilon$$

Solution Steps

The factorial of 1 is 1.

$$\frac{2\epsilon }{1}\times 1$$

Anything divided by one gives itself.

$$2\epsilon \times 1$$

Multiply 2 and 1 to get 2.

$$2\epsilon$$

Differentiate w.r.t. ε

$$2$$

Steps Using Definition of a Derivative

The factorial of 1 is 1.

$$\frac{\mathrm{d}}{\mathrm{d}\epsilon }(\frac{2\epsilon }{1}\times 1)$$

Anything divided by one gives itself.

$$\frac{\mathrm{d}}{\mathrm{d}\epsilon }(2\epsilon \times 1)$$

Multiply 2 and 1 to get 2.

$$\frac{\mathrm{d}}{\mathrm{d}\epsilon }(2\epsilon )$$

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

$$2\epsilon ^{1-1}$$

Subtract 1 from 1.

$$2\epsilon ^{0}$$

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

$$2\times 1$$

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

$$2$$