Solve x^-1/(1)2^

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

Evaluate

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

Solution Steps

Calculate 2 to the power of 1 and get 2.

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

Multiply 1 and 2 to get 2.

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

Differentiate w.r.t. x

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

Steps Using Definition of a Derivative

Calculate 2 to the power of 1 and get 2.

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

Multiply 1 and 2 to get 2.

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

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

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

Subtract 1 from -1.

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