Solve 2mquadtext{(2)}5/2m

$$2 m \quad \text { (2) } \frac { 5 } { 2 } m$$

Evaluate

$$10m^{2}$$

Solution Steps

Multiply m and m to get m^{2}.

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

Multiply 2 and 2 to get 4.

$$4m^{2}\times \frac{5}{2}$$

Express 4\times \frac{5}{2} as a single fraction.

$$\frac{4\times 5}{2}m^{2}$$

Multiply 4 and 5 to get 20.

$$\frac{20}{2}m^{2}$$

Divide 20 by 2 to get 10.

$$10m^{2}$$

Differentiate w.r.t. m

$$20m$$

Steps Using Definition of a Derivative

Multiply m and m to get m^{2}.

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

Multiply 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}m}(4m^{2}\times \frac{5}{2})$$

Express 4\times \frac{5}{2} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{4\times 5}{2}m^{2})$$

Multiply 4 and 5 to get 20.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{20}{2}m^{2})$$

Divide 20 by 2 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}m}(10m^{2})$$

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

$$2\times 10m^{2-1}$$

Multiply 2 times 10.

$$20m^{2-1}$$

Subtract 1 from 2.

$$20m^{1}$$

For any term t, t^{1}=t.

$$20m$$