Solve x^-1/(1)^-1

$$\frac { x ^ { - 1 } } { ( 1 ) ^ { - 1 } }$$

Evaluate

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

Solution Steps

Calculate 1 to the power of -1 and get 1.

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

Anything divided by one gives itself.

$$x^{-1}$$

Differentiate w.r.t. x

$$-\frac{1}{x^{2}}$$

Steps Using Definition of a Derivative

Calculate 1 to the power of -1 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{-1}}{1})$$

Anything divided by one gives itself.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{-1})$$

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

$$-x^{-1-1}$$

Subtract 1 from -1.

$$-x^{-2}$$