Solve 1/5mxm

$$\frac { 1 } { 5 m } x m$$

Evaluate

$$\frac{x}{5}$$

Solution Steps

Express \frac{1}{5m}x as a single fraction.

$$\frac{x}{5m}m$$

Express \frac{x}{5m}m as a single fraction.

$$\frac{xm}{5m}$$

Cancel out m in both numerator and denominator.

$$\frac{x}{5}$$

Differentiate w.r.t. x

$$\frac{1}{5} = 0.2$$

Steps Using Definition of a Derivative

Express \frac{1}{5m}x as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{5m}m)$$

Express \frac{x}{5m}m as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{xm}{5m})$$

Cancel out m in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{5})$$

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

$$\frac{1}{5}x^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{5}x^{0}$$

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

$$\frac{1}{5}\times 1$$

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

$$\frac{1}{5}$$