Solve m^-5*m^-8/2

$$\frac { m ^ { - 5 } \cdot m ^ { - 8 } } { 2 }$$

Differentiate w.r.t. m

$$-\frac{13}{2m^{14}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -5 and -8 to get -13.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{m^{-13}}{2})$$

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

$$-13\times \frac{1}{2}m^{-13-1}$$

Multiply -13 times \frac{1}{2}.

$$-\frac{13}{2}m^{-13-1}$$

Subtract 1 from -13.

$$-\frac{13}{2}m^{-14}$$

Evaluate

$$\frac{1}{2m^{13}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -5 and -8 to get -13.

$$\frac{m^{-13}}{2}$$