Solve (3m)(-2.5m^2)=

$$( 3 m ) ( - 2.5 m ^ { 2 } ) =$$

Evaluate

$$-\frac{15m^{3}}{2}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$3m^{3}\left(-2.5\right)$$

Multiply 3 and -2.5 to get -7.5.

$$-7.5m^{3}$$

Differentiate w.r.t. m

$$-\frac{45m^{2}}{2}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}m}(3m^{3}\left(-2.5\right))$$

Multiply 3 and -2.5 to get -7.5.

$$\frac{\mathrm{d}}{\mathrm{d}m}(-7.5m^{3})$$

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

$$3\left(-7.5\right)m^{3-1}$$

Multiply 3 times -7.5.

$$-22.5m^{3-1}$$

Subtract 1 from 3.

$$-22.5m^{2}$$