Solve (-3n^3+3n^2+n+1)

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

Differentiate w.r.t. n

$$1+6n-9n^{2}$$

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}.

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

Multiply 3 times -3.

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

Subtract 1 from 3.

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

Multiply 2 times 3.

$$-9n^{2}+6n^{2-1}+n^{1-1}$$

Subtract 1 from 2.

$$-9n^{2}+6n^{1}+n^{1-1}$$

Subtract 1 from 1.

$$-9n^{2}+6n^{1}+n^{0}$$

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

$$-9n^{2}+6n+n^{0}$$

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

$$-9n^{2}+6n+1$$

Evaluate

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