Solve a-a^2-1+a+a^2+3a+2a+6

$$a - a ^ { 2 } - 1 + a + a ^ { 2 } + 3 a + 2 a + 6$$

Evaluate

$$7a+5$$

Solution Steps

Combine a and a to get 2a.

$$2a-a^{2}-1+a^{2}+3a+2a+6$$

Combine -a^{2} and a^{2} to get 0.

$$2a-1+3a+2a+6$$

Combine 2a and 3a to get 5a.

$$5a-1+2a+6$$

Combine 5a and 2a to get 7a.

$$7a-1+6$$

Add -1 and 6 to get 5.

$$7a+5$$

Differentiate w.r.t. a

$$7$$

Steps Using Derivative Rule for Sum

Combine a and a to get 2a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(2a-a^{2}-1+a^{2}+3a+2a+6)$$

Combine -a^{2} and a^{2} to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}a}(2a-1+3a+2a+6)$$

Combine 2a and 3a to get 5a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(5a-1+2a+6)$$

Combine 5a and 2a to get 7a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(7a-1+6)$$

Add -1 and 6 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}a}(7a+5)$$

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}.

$$7a^{1-1}$$

Subtract 1 from 1.

$$7a^{0}$$

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

$$7\times 1$$

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

$$7$$