Solve -2x^-3*-2x^-1

$$- 2 x ^ { - 3 } \cdot - 2 x ^ { - 1 }$$

Evaluate

$$\frac{4}{x^{4}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -3 and -1 to get -4.

$$-2x^{-4}\left(-2\right)$$

Multiply -2 and -2 to get 4.

$$4x^{-4}$$

Differentiate w.r.t. x

$$-\frac{16}{x^{5}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -3 and -1 to get -4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-2x^{-4}\left(-2\right))$$

Multiply -2 and -2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{-4})$$

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

$$-4\times 4x^{-4-1}$$

Multiply -4 times 4.

$$-16x^{-4-1}$$

Subtract 1 from -4.

$$-16x^{-5}$$