Solve varepsilon/22-2/1varepsilon

$$\frac { \varepsilon } { 2 } 2 - \frac { 2 } { 1 } \varepsilon$$

Evaluate

$$-\epsilon$$

Solution Steps

Cancel out 2 and 2.

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

Anything divided by one gives itself.

$$\epsilon -2\epsilon$$

Combine \epsilon and -2\epsilon to get -\epsilon .

$$-\epsilon$$

Differentiate w.r.t. ε

$$-1$$

Steps Using Definition of a Derivative

Cancel out 2 and 2.

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

Anything divided by one gives itself.

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

Combine \epsilon and -2\epsilon to get -\epsilon .

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

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

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

Subtract 1 from 1.

$$-\epsilon ^{0}$$

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

$$-1$$