Solve 7a^2+3a+a^3+3a^2+6

$$7 a ^ { 2 } + 3 a + a ^ { 3 } + 3 a ^ { 2 } + 6$$

Differentiate w.r.t. a

$$3a^{2}+20a+3$$

Steps Using Derivative Rule for Sum

Combine 7a^{2} and 3a^{2} to get 10a^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(10a^{2}+3a+a^{3}+6)$$

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}.

$$2\times 10a^{2-1}+3a^{1-1}+3a^{3-1}$$

Multiply 2 times 10.

$$20a^{2-1}+3a^{1-1}+3a^{3-1}$$

Subtract 1 from 2.

$$20a^{1}+3a^{1-1}+3a^{3-1}$$

Subtract 1 from 1.

$$20a^{1}+3a^{0}+3a^{3-1}$$

Subtract 1 from 3.

$$20a^{1}+3a^{0}+3a^{2}$$

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

$$20a+3a^{0}+3a^{2}$$

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

$$20a+3\times 1+3a^{2}$$

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

$$20a+3+3a^{2}$$

Evaluate

$$a^{3}+10a^{2}+3a+6$$

Solution Steps

Combine 7a^{2} and 3a^{2} to get 10a^{2}.

$$10a^{2}+3a+a^{3}+6$$