Solve 4x^-5*-6x^-6

$$4 x ^ { - 5 } \cdot - 6 x ^ { - 6 }$$

Evaluate

$$-\frac{24}{x^{11}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -5 and -6 to get -11.

$$4x^{-11}\left(-6\right)$$

Multiply 4 and -6 to get -24.

$$-24x^{-11}$$

Differentiate w.r.t. x

$$\frac{264}{x^{12}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -5 and -6 to get -11.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{-11}\left(-6\right))$$

Multiply 4 and -6 to get -24.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-24x^{-11})$$

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

$$-11\left(-24\right)x^{-11-1}$$

Multiply -11 times -24.

$$264x^{-11-1}$$

Subtract 1 from -11.

$$264x^{-12}$$