Solve =3n^{4}+6n^3+3n^2+20n^3+30n+1+42n^2+42n+36n

$$= 3 n ^ { 4 } + 6 n ^ { 3 } + 3 n ^ { 2 } + 20 n ^ { 3 } + 30 n + 1 + 42 n ^ { 2 } + 42 n + 36 n$$

Evaluate

$$3n^{4}+26n^{3}+45n^{2}+108n+1$$

Solution Steps

Combine 6n^{3} and 20n^{3} to get 26n^{3}.

$$3n^{4}+26n^{3}+3n^{2}+30n+1+42n^{2}+42n+36n$$

Combine 3n^{2} and 42n^{2} to get 45n^{2}.

$$3n^{4}+26n^{3}+45n^{2}+30n+1+42n+36n$$

Combine 30n and 42n to get 72n.

$$3n^{4}+26n^{3}+45n^{2}+72n+1+36n$$

Combine 72n and 36n to get 108n.

$$3n^{4}+26n^{3}+45n^{2}+108n+1$$

Differentiate w.r.t. n

$$12n^{3}+78n^{2}+90n+108$$