Solve -5+m+12+(-5m+2+-6

$$- 5 + m + 12 + ( - 5 m + 2 + - 6$$

Evaluate

$$3-4m$$

Solution Steps

Add -5 and 12 to get 7.

$$7+m-5m+2-6$$

Combine m and -5m to get -4m.

$$7-4m+2-6$$

Add 7 and 2 to get 9.

$$9-4m-6$$

Subtract 6 from 9 to get 3.

$$3-4m$$

Differentiate w.r.t. m

$$-4$$

Steps Using Derivative Rule for Sum

Add -5 and 12 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}m}(7+m-5m+2-6)$$

Combine m and -5m to get -4m.

$$\frac{\mathrm{d}}{\mathrm{d}m}(7-4m+2-6)$$

Add 7 and 2 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}m}(9-4m-6)$$

Subtract 6 from 9 to get 3.

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

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$-4m^{1-1}$$

Subtract 1 from 1.

$$-4m^{0}$$

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

$$-4$$