Solve 2a+4-3a+6-2a+8a-8

$$2a+4-3a+6-2a+8a-8$$

Evaluate

$$5a+2$$

Solution Steps

Combine 2a and -3a to get -a.

$$-a+4+6-2a+8a-8$$

Add 4 and 6 to get 10.

$$-a+10-2a+8a-8$$

Combine -a and -2a to get -3a.

$$-3a+10+8a-8$$

Combine -3a and 8a to get 5a.

$$5a+10-8$$

Subtract 8 from 10 to get 2.

$$5a+2$$

Differentiate w.r.t. a

$$5$$

Steps Using Derivative Rule for Sum

Combine 2a and -3a to get -a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-a+4+6-2a+8a-8)$$

Add 4 and 6 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-a+10-2a+8a-8)$$

Combine -a and -2a to get -3a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-3a+10+8a-8)$$

Combine -3a and 8a to get 5a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(5a+10-8)$$

Subtract 8 from 10 to get 2.

$$\frac{\mathrm{d}}{\mathrm{d}a}(5a+2)$$

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}.

$$5a^{1-1}$$

Subtract 1 from 1.

$$5a^{0}$$

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

$$5\times 1$$

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

$$5$$