Solve x/frac{2x{x}}

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

Evaluate

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

Solution Steps

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

$$\frac{xx}{2x}$$

Cancel out x in both numerator and denominator.

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

Differentiate w.r.t. x

$$\frac{1}{2} = 0.5$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{xx}{2x})$$

Cancel out x in both numerator and denominator.

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

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

$$\frac{1}{2}x^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{2}x^{0}$$

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

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

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

$$\frac{1}{2}$$