Solve (a^2+a+1)+(5a^2-8a+20)

$$( a ^ { 2 } + a + 1 ) + ( 5 a ^ { 2 } - 8 a + 20 )$$

Evaluate

$$6a^{2}-7a+21$$

Solution Steps

Combine a^{2} and 5a^{2} to get 6a^{2}.

$$6a^{2}+a+1-8a+20$$

Combine a and -8a to get -7a.

$$6a^{2}-7a+1+20$$

Add 1 and 20 to get 21.

$$6a^{2}-7a+21$$

Differentiate w.r.t. a

$$12a-7$$

Steps Using Derivative Rule for Sum

Combine a^{2} and 5a^{2} to get 6a^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(6a^{2}+a+1-8a+20)$$

Combine a and -8a to get -7a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(6a^{2}-7a+1+20)$$

Add 1 and 20 to get 21.

$$\frac{\mathrm{d}}{\mathrm{d}a}(6a^{2}-7a+21)$$

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}.

$$2\times 6a^{2-1}-7a^{1-1}$$

Multiply 2 times 6.

$$12a^{2-1}-7a^{1-1}$$

Subtract 1 from 2.

$$12a^{1}-7a^{1-1}$$

Subtract 1 from 1.

$$12a^{1}-7a^{0}$$

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

$$12a-7a^{0}$$

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

$$12a-7$$