Solve (-6x^-9)(-2x^-4)

$$( - 6 x ^ { - 9 } ) ( - 2 x ^ { - 4 } )$$

Evaluate

$$\frac{12}{x^{13}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -9 and -4 to get -13.

$$-6x^{-13}\left(-2\right)$$

Multiply -6 and -2 to get 12.

$$12x^{-13}$$

Differentiate w.r.t. x

$$-\frac{156}{x^{14}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -9 and -4 to get -13.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-6x^{-13}\left(-2\right))$$

Multiply -6 and -2 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x^{-13})$$

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

$$-13\times 12x^{-13-1}$$

Multiply -13 times 12.

$$-156x^{-13-1}$$

Subtract 1 from -13.

$$-156x^{-14}$$