Solve -1/xdx

$$- \frac { 1 } { x } d x$$

Evaluate

$$-d$$

Solution Steps

Express \left(-\frac{1}{x}\right)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

Express \left(-\frac{1}{x}\right)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.

$$-1$$