Solve (-4x)(-6x^-4)

$$(-4x)(-6 { x }^{ -4 } )$$

Evaluate

$$\frac{24}{x^{3}}$$

Solution Steps

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

$$-4x^{-3}\left(-6\right)$$

Multiply -4 and -6 to get 24.

$$24x^{-3}$$

Differentiate w.r.t. x

$$-\frac{72}{x^{4}}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(-4x^{-3}\left(-6\right))$$

Multiply -4 and -6 to get 24.

$$\frac{\mathrm{d}}{\mathrm{d}x}(24x^{-3})$$

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

$$-3\times 24x^{-3-1}$$

Multiply -3 times 24.

$$-72x^{-3-1}$$

Subtract 1 from -3.

$$-72x^{-4}$$