Solve -21x/2+11x

$$- \frac{ 21x }{ 2 } +11x$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 11x times \frac{2}{2}.

$$-\frac{21x}{2}+\frac{2\times 11x}{2}$$

Since -\frac{21x}{2} and \frac{2\times 11x}{2} have the same denominator, add them by adding their numerators.

$$\frac{-21x+2\times 11x}{2}$$

Do the multiplications in -21x+2\times 11x.

$$\frac{-21x+22x}{2}$$

Combine like terms in -21x+22x.

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

Differentiate w.r.t. x

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

Steps Using Definition of a Derivative

To add or subtract expressions, expand them to make their denominators the same. Multiply 11x times \frac{2}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{21x}{2}+\frac{2\times 11x}{2})$$

Since -\frac{21x}{2} and \frac{2\times 11x}{2} have the same denominator, add them by adding their numerators.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-21x+2\times 11x}{2})$$

Do the multiplications in -21x+2\times 11x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-21x+22x}{2})$$

Combine like terms in -21x+22x.

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

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.

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