Solve 4n^6+7n^2+1

$$4 n ^ { 6 } + 7 n ^ { 2 } + 1$$

Differentiate w.r.t. n

$$24n^{5}+14n$$

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}.

$$6\times 4n^{6-1}+2\times 7n^{2-1}$$

Multiply 6 times 4.

$$24n^{6-1}+2\times 7n^{2-1}$$

Subtract 1 from 6.

$$24n^{5}+2\times 7n^{2-1}$$

Multiply 2 times 7.

$$24n^{5}+14n^{2-1}$$

Subtract 1 from 2.

$$24n^{5}+14n^{1}$$

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

$$24n^{5}+14n$$

Evaluate

$$4n^{6}+7n^{2}+1$$