Solve x-x+x/x^2dx

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

Evaluate

$$d$$

Solution Steps

Combine x and -x to get 0.

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

Cancel out x in both numerator and denominator.

$$\frac{1}{x}dx$$

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

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

Cancel out x and x.

$$d$$

Differentiate w.r.t. d

$$1$$

Steps Using Definition of a Derivative

Combine x and -x to get 0.

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

Cancel out x in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{1}{x}dx)$$

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

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

Cancel out x and x.

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

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

$$d^{1-1}$$

Subtract 1 from 1.

$$d^{0}$$

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

$$1$$