Solve (3-a+a^2)+(3+2a-2a)

$$( 3 - a + a ^ { 2 } ) + ( 3 + 2 a - 2 a )$$

Evaluate

$$a^{2}-a+6$$

Solution Steps

Add 3 and 3 to get 6.

$$6-a+a^{2}+2a-2a$$

Combine -a and 2a to get a.

$$6+a+a^{2}-2a$$

Combine a and -2a to get -a.

$$6-a+a^{2}$$

Differentiate w.r.t. a

$$2a-1$$

Steps Using Derivative Rule for Sum

Add 3 and 3 to get 6.

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

Combine -a and 2a to get a.

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

Combine a and -2a to get -a.

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

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}.

$$-a^{1-1}+2a^{2-1}$$

Subtract 1 from 1.

$$-a^{0}+2a^{2-1}$$

Subtract 1 from 2.

$$-a^{0}+2a^{1}$$

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

$$-a^{0}+2a$$

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

$$-1+2a$$