Solve (-2x)^-1

$$( - 2 x ) ^ { - 1 }$$

Evaluate

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

Solution Steps

Expand \left(-2x\right)^{-1}.

$$\left(-2\right)^{-1}x^{-1}$$

Calculate -2 to the power of -1 and get -\frac{1}{2}.

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

Differentiate w.r.t. x

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

Steps Using Definition of a Derivative

Expand \left(-2x\right)^{-1}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-2\right)^{-1}x^{-1})$$

Calculate -2 to the power of -1 and get -\frac{1}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{1}{2}x^{-1})$$

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

$$-\left(-\frac{1}{2}\right)x^{-1-1}$$

Multiply -1 times -\frac{1}{2}.

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

Subtract 1 from -1.

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