Solve n^3-n^2+3n+2

$$n ^ { 3 } - n ^ { 2 } + 3 n + 2$$

Differentiate w.r.t. n

$$3n^{2}-2n+3$$

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}.

$$3n^{3-1}+2\left(-1\right)n^{2-1}+3n^{1-1}$$

Subtract 1 from 3.

$$3n^{2}+2\left(-1\right)n^{2-1}+3n^{1-1}$$

Multiply 2 times -1.

$$3n^{2}-2n^{2-1}+3n^{1-1}$$

Subtract 1 from 2.

$$3n^{2}-2n^{1}+3n^{1-1}$$

Subtract 1 from 1.

$$3n^{2}-2n^{1}+3n^{0}$$

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

$$3n^{2}-2n+3n^{0}$$

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

$$3n^{2}-2n+3\times 1$$

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

$$3n^{2}-2n+3$$

Evaluate

$$n^{3}-n^{2}+3n+2$$