Solve 4x^-3*4x

$$4 x ^ { - 3 } \cdot 4 x$$

Evaluate

$$\frac{16}{x^{2}}$$

Solution Steps

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

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

Multiply 4 and 4 to get 16.

$$16x^{-2}$$

Differentiate w.r.t. x

$$-\frac{32}{x^{3}}$$

Steps Using Definition of a Derivative

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

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

Multiply 4 and 4 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(16x^{-2})$$

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

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

Multiply -2 times 16.

$$-32x^{-2-1}$$

Subtract 1 from -2.

$$-32x^{-3}$$