Solve x+2^-1x-x

$$x + 2 ^ { - 1 } x - x$$

Evaluate

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

Solution Steps

Calculate 2 to the power of -1 and get \frac{1}{2}.

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

Combine x and \frac{1}{2}x to get \frac{3}{2}x.

$$\frac{3}{2}x-x$$

Combine \frac{3}{2}x and -x to get \frac{1}{2}x.

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

Differentiate w.r.t. x

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

Steps Using Definition of a Derivative

Calculate 2 to the power of -1 and get \frac{1}{2}.

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

Combine x and \frac{1}{2}x to get \frac{3}{2}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{2}x-x)$$

Combine \frac{3}{2}x and -x to get \frac{1}{2}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{2}x)$$

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.

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