Solve x-9x/10

$$x - \frac { 9 x } { 10 }$$

Evaluate

$$\frac{x}{10}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{10}{10}.

$$\frac{10x}{10}-\frac{9x}{10}$$

Since \frac{10x}{10} and \frac{9x}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10x-9x}{10}$$

Combine like terms in 10x-9x.

$$\frac{x}{10}$$

Differentiate w.r.t. x

$$\frac{1}{10} = 0.1$$

Steps Using Definition of a Derivative

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{10}{10}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{10x}{10}-\frac{9x}{10})$$

Since \frac{10x}{10} and \frac{9x}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{10x-9x}{10})$$

Combine like terms in 10x-9x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{10})$$

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

$$\frac{1}{10}x^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{10}x^{0}$$

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

$$\frac{1}{10}\times 1$$

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

$$\frac{1}{10}$$