Solve (-x)^-frac{3{3}}

$$( - x ) ^ { - \frac { 3 } { 3 } }$$

Evaluate

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

Solution Steps

Divide 3 by 3 to get 1.

$$\left(-x\right)^{-1}$$

Expand \left(-x\right)^{-1}.

$$\left(-1\right)^{-1}x^{-1}$$

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

$$-x^{-1}$$

Differentiate w.r.t. x

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

Steps Using Definition of a Derivative

Divide 3 by 3 to get 1.

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

Expand \left(-x\right)^{-1}.

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

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

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

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

$$-\left(-1\right)x^{-1-1}$$

Multiply -1 times -1.

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

Subtract 1 from -1.

$$x^{-2}$$