Solve 2/x/frac{2{x^2}}

$$\frac { \frac { 2 } { x } } { \frac { 2 } { x ^ { 2 } } }$$

Evaluate

$$x$$

Solution Steps

Divide \frac{2}{x} by \frac{2}{x^{2}} by multiplying \frac{2}{x} by the reciprocal of \frac{2}{x^{2}}.

$$\frac{2x^{2}}{x\times 2}$$

Cancel out 2x in both numerator and denominator.

$$x$$

Differentiate w.r.t. x

$$1$$

Steps Using Definition of a Derivative

Divide \frac{2}{x} by \frac{2}{x^{2}} by multiplying \frac{2}{x} by the reciprocal of \frac{2}{x^{2}}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x^{2}}{x\times 2})$$

Cancel out 2x in both numerator and denominator.

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

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

$$x^{1-1}$$

Subtract 1 from 1.

$$x^{0}$$

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

$$1$$