Solve 3a^3+10a^2+3a+2

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

Differentiate w.r.t. a

$$9a^{2}+20a+3$$

Steps Using Derivative Rule for Sum

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}.

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

Multiply 3 times 3.

$$9a^{3-1}+2\times 10a^{2-1}+3a^{1-1}$$

Subtract 1 from 3.

$$9a^{2}+2\times 10a^{2-1}+3a^{1-1}$$

Multiply 2 times 10.

$$9a^{2}+20a^{2-1}+3a^{1-1}$$

Subtract 1 from 2.

$$9a^{2}+20a^{1}+3a^{1-1}$$

Subtract 1 from 1.

$$9a^{2}+20a^{1}+3a^{0}$$

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

$$9a^{2}+20a+3a^{0}$$

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

$$9a^{2}+20a+3\times 1$$

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

$$9a^{2}+20a+3$$

Evaluate

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