Solve 2m/9+4m/9=

$$\frac { 2 m } { 9 } + \frac { 4 m } { 9 } =$$

Evaluate

$$\frac{2m}{3}$$

Short Solution Steps

Since \frac{2m}{9} and \frac{4m}{9} have the same denominator, add them by adding their numerators.

$$\frac{2m+4m}{9}$$

Combine like terms in 2m+4m.

$$\frac{6m}{9}$$

Divide 6m by 9 to get \frac{2}{3}m.

$$\frac{2}{3}m$$

Differentiate w.r.t. m

$$\frac{2}{3} = 0.6666666666666666$$

Steps Using Definition of a Derivative

Since \frac{2m}{9} and \frac{4m}{9} have the same denominator, add them by adding their numerators.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{2m+4m}{9})$$

Combine like terms in 2m+4m.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{6m}{9})$$

Divide 6m by 9 to get \frac{2}{3}m.

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

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

$$\frac{2}{3}m^{1-1}$$

Subtract 1 from 1.

$$\frac{2}{3}m^{0}$$

For any term t except 0, t^{0}=1.

$$\frac{2}{3}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{2}{3}$$