Solve a^2+3a+5a+6+8a^2

$$a ^ { 2 } + 3 a + 5 a + 6 + 8 a ^ { 2 }$$

Evaluate

$$9a^{2}+8a+6$$

Solution Steps

Combine 3a and 5a to get 8a.

$$a^{2}+8a+6+8a^{2}$$

Combine a^{2} and 8a^{2} to get 9a^{2}.

$$9a^{2}+8a+6$$

Differentiate w.r.t. a

$$18a+8$$

Steps Using Derivative Rule for Sum

Combine 3a and 5a to get 8a.

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

Combine a^{2} and 8a^{2} to get 9a^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(9a^{2}+8a+6)$$

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}.

$$2\times 9a^{2-1}+8a^{1-1}$$

Multiply 2 times 9.

$$18a^{2-1}+8a^{1-1}$$

Subtract 1 from 2.

$$18a^{1}+8a^{1-1}$$

Subtract 1 from 1.

$$18a^{1}+8a^{0}$$

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

$$18a+8a^{0}$$

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

$$18a+8\times 1$$

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

$$18a+8$$