Solve 4x*2x^-3

$$4 x \times 2 x ^ { - 3 }$$

Evaluate

$$\frac{8}{x^{2}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and -3 to get -2.

$$4x^{-2}\times 2$$

Multiply 4 and 2 to get 8.

$$8x^{-2}$$

Differentiate w.r.t. x

$$-\frac{16}{x^{3}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and -3 to get -2.

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

Multiply 4 and 2 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x^{-2})$$

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

$$-2\times 8x^{-2-1}$$

Multiply -2 times 8.

$$-16x^{-2-1}$$

Subtract 1 from -2.

$$-16x^{-3}$$