Solve 3m^5*-8m^2

$$3 m ^ { 5 } \cdot - 8 m ^ { 2 }$$

Evaluate

$$-24m^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$3m^{7}\left(-8\right)$$

Multiply 3 and -8 to get -24.

$$-24m^{7}$$

Differentiate w.r.t. m

$$-168m^{6}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}m}(3m^{7}\left(-8\right))$$

Multiply 3 and -8 to get -24.

$$\frac{\mathrm{d}}{\mathrm{d}m}(-24m^{7})$$

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

$$7\left(-24\right)m^{7-1}$$

Multiply 7 times -24.

$$-168m^{7-1}$$

Subtract 1 from 7.

$$-168m^{6}$$