Solve 3a^2+8a-2--4a^2-2a+6

$$3 { a }^{ 2 } +8a-2--4 { a }^{ 2 } -2a+6$$

Evaluate

$$7a^{2}+6a+4$$

Solution Steps

The opposite of -4a^{2} is 4a^{2}.

$$3a^{2}+8a-2+4a^{2}-2a+6$$

Combine 3a^{2} and 4a^{2} to get 7a^{2}.

$$7a^{2}+8a-2-2a+6$$

Combine 8a and -2a to get 6a.

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

Add -2 and 6 to get 4.

$$7a^{2}+6a+4$$

Differentiate w.r.t. a

$$14a+6$$

Steps Using Derivative Rule for Sum

The opposite of -4a^{2} is 4a^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(3a^{2}+8a-2+4a^{2}-2a+6)$$

Combine 3a^{2} and 4a^{2} to get 7a^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(7a^{2}+8a-2-2a+6)$$

Combine 8a and -2a to get 6a.

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

Add -2 and 6 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}a}(7a^{2}+6a+4)$$

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}.

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

Multiply 2 times 7.

$$14a^{2-1}+6a^{1-1}$$

Subtract 1 from 2.

$$14a^{1}+6a^{1-1}$$

Subtract 1 from 1.

$$14a^{1}+6a^{0}$$

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

$$14a+6a^{0}$$

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

$$14a+6\times 1$$

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

$$14a+6$$