Solve 3n^3-26n^2+51n+19

$$3 n ^ { 3 } - 26 n ^ { 2 } + 51 n + 19$$

Differentiate w.r.t. n

$$9n^{2}-52n+51$$

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}.

$$3\times 3n^{3-1}+2\left(-26\right)n^{2-1}+51n^{1-1}$$

Multiply 3 times 3.

$$9n^{3-1}+2\left(-26\right)n^{2-1}+51n^{1-1}$$

Subtract 1 from 3.

$$9n^{2}+2\left(-26\right)n^{2-1}+51n^{1-1}$$

Multiply 2 times -26.

$$9n^{2}-52n^{2-1}+51n^{1-1}$$

Subtract 1 from 2.

$$9n^{2}-52n^{1}+51n^{1-1}$$

Subtract 1 from 1.

$$9n^{2}-52n^{1}+51n^{0}$$

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

$$9n^{2}-52n+51n^{0}$$

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

$$9n^{2}-52n+51\times 1$$

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

$$9n^{2}-52n+51$$

Evaluate

$$3n^{3}-26n^{2}+51n+19$$