Solve (8a^2-3-7a)+(2a+5+4a^2)

$$( 8 a ^ { 2 } - 3 - 7 a ) + ( 2 a + 5 + 4 a ^ { 2 } )$$

Evaluate

$$12a^{2}-5a+2$$

Solution Steps

Combine -7a and 2a to get -5a.

$$8a^{2}-3-5a+5+4a^{2}$$

Add -3 and 5 to get 2.

$$8a^{2}+2-5a+4a^{2}$$

Combine 8a^{2} and 4a^{2} to get 12a^{2}.

$$12a^{2}+2-5a$$

Differentiate w.r.t. a

$$24a-5$$

Steps Using Derivative Rule for Sum

Combine -7a and 2a to get -5a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(8a^{2}-3-5a+5+4a^{2})$$

Add -3 and 5 to get 2.

$$\frac{\mathrm{d}}{\mathrm{d}a}(8a^{2}+2-5a+4a^{2})$$

Combine 8a^{2} and 4a^{2} to get 12a^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(12a^{2}+2-5a)$$

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}.

$$2\times 12a^{2-1}-5a^{1-1}$$

Multiply 2 times 12.

$$24a^{2-1}-5a^{1-1}$$

Subtract 1 from 2.

$$24a^{1}-5a^{1-1}$$

Subtract 1 from 1.

$$24a^{1}-5a^{0}$$

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

$$24a-5a^{0}$$

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

$$24a-5$$