Solve (5m)(2m^2)=

$$( 5 m ) ( 2 m ^ { 2 } ) =$$

Evaluate

$$10m^{3}$$

Solution Steps

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

$$5m^{3}\times 2$$

Multiply 5 and 2 to get 10.

$$10m^{3}$$

Differentiate w.r.t. m

$$30m^{2}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}m}(5m^{3}\times 2)$$

Multiply 5 and 2 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}m}(10m^{3})$$

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

$$3\times 10m^{3-1}$$

Multiply 3 times 10.

$$30m^{3-1}$$

Subtract 1 from 3.

$$30m^{2}$$