Solve 2x*-x^-2

$$2 x \cdot - x ^ { - 2 }$$

Evaluate

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

Solution Steps

Multiply 2 and -1 to get -2.

$$-2xx^{-2}$$

To multiply powers of the same base, add their exponents. Add 1 and -2 to get -1.

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

Differentiate w.r.t. x

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

Steps Using Definition of a Derivative

Multiply 2 and -1 to get -2.

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

To multiply powers of the same base, add their exponents. Add 1 and -2 to get -1.

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

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

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

Multiply -1 times -2.

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

Subtract 1 from -1.

$$2x^{-2}$$