Solve 4n^2+2n+1

$$4 { n }^{ 2 } +2n+1$$

Differentiate w.r.t. n

$$8n+2$$

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}.

$$2\times 4n^{2-1}+2n^{1-1}$$

Multiply 2 times 4.

$$8n^{2-1}+2n^{1-1}$$

Subtract 1 from 2.

$$8n^{1}+2n^{1-1}$$

Subtract 1 from 1.

$$8n^{1}+2n^{0}$$

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

$$8n+2n^{0}$$

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

$$8n+2\times 1$$

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

$$8n+2$$

Evaluate

$$4n^{2}+2n+1$$