Solve P(m)=10m-6m-m-(-4m)

$$P ( m ) = 10 m - 6 m - m - ( - 4 m )$$

Evaluate

$$7m$$

Solution Steps

Combine 10m and -6m to get 4m.

$$4m-m-\left(-4m\right)$$

Combine 4m and -m to get 3m.

$$3m-\left(-4m\right)$$

The opposite of -4m is 4m.

$$3m+4m$$

Combine 3m and 4m to get 7m.

$$7m$$

Differentiate w.r.t. m

$$7$$

Steps Using Definition of a Derivative

Combine 10m and -6m to get 4m.

$$\frac{\mathrm{d}}{\mathrm{d}m}(4m-m-\left(-4m\right))$$

Combine 4m and -m to get 3m.

$$\frac{\mathrm{d}}{\mathrm{d}m}(3m-\left(-4m\right))$$

The opposite of -4m is 4m.

$$\frac{\mathrm{d}}{\mathrm{d}m}(3m+4m)$$

Combine 3m and 4m to get 7m.

$$\frac{\mathrm{d}}{\mathrm{d}m}(7m)$$

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

$$7m^{1-1}$$

Subtract 1 from 1.

$$7m^{0}$$

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

$$7\times 1$$

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

$$7$$