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

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

Evaluate

$$a^{2}-2a+4$$

Solution Steps

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

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

Add 2 and 2 to get 4.

$$a^{2}-2a+4$$

Differentiate w.r.t. a

$$2\left(a-1\right)$$

Steps Using Derivative Rule for Sum

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

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

Add 2 and 2 to get 4.

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

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}.

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

Subtract 1 from 2.

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

Subtract 1 from 1.

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

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

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

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

$$2a-2$$