Solve 2x/x^2dx

$$\frac { 2 x } { x ^ { 2 } } d x$$

Evaluate

$$2d$$

Solution Steps

Cancel out x in both numerator and denominator.

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

Express \frac{2}{x}d as a single fraction.

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

Cancel out x and x.

$$2d$$

Differentiate w.r.t. d

$$2$$

Steps Using Definition of a Derivative

Cancel out x in both numerator and denominator.

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

Express \frac{2}{x}d as a single fraction.

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

Cancel out x and x.

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

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

$$2d^{1-1}$$

Subtract 1 from 1.

$$2d^{0}$$

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

$$2\times 1$$

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

$$2$$