Solve =-n^3-n^2-2n+1

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

Differentiate w.r.t. n

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

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}.

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

Multiply 3 times -1.

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

Subtract 1 from 3.

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

Multiply 2 times -1.

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

Subtract 1 from 2.

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

Subtract 1 from 1.

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

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

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

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

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

Evaluate

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