Solve 4m+3/2m+7/2m-6m

$$4 m + \frac { 3 } { 2 } m + \frac { 7 } { 2 } m - 6 m$$

Evaluate

$$3m$$

Solution Steps

Combine 4m and \frac{3}{2}m to get \frac{11}{2}m.

$$\frac{11}{2}m+\frac{7}{2}m-6m$$

Combine \frac{11}{2}m and \frac{7}{2}m to get 9m.

$$9m-6m$$

Combine 9m and -6m to get 3m.

$$3m$$

Differentiate w.r.t. m

$$3$$

Steps Using Definition of a Derivative

Combine 4m and \frac{3}{2}m to get \frac{11}{2}m.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{11}{2}m+\frac{7}{2}m-6m)$$

Combine \frac{11}{2}m and \frac{7}{2}m to get 9m.

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

Combine 9m and -6m to get 3m.

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

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

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

Subtract 1 from 1.

$$3m^{0}$$

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

$$3\times 1$$

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

$$3$$