Solve 3x/4-x/4

$$\frac { 3 x } { 4 } - \frac { x } { 4 }$$

Evaluate

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

Short Solution Steps

Since \frac{3x}{4} and \frac{x}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3x-x}{4}$$

Combine like terms in 3x-x.

$$\frac{2x}{4}$$

Divide 2x by 4 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

Since \frac{3x}{4} and \frac{x}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3x-x}{4})$$

Combine like terms in 3x-x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x}{4})$$

Divide 2x by 4 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.

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