Solve (9r^{4}+7r^{3}+7r^2+7r+2)+(6r^4+2r^3+7r^2)

$$( 9 r ^ { 4 } + 7 r ^ { 3 } + 7 r ^ { 2 } + 7 r + 2 ) + ( 6 r ^ { 4 } + 2 r ^ { 3 } + 7 r ^ { 2 } )$$

Evaluate

$$15r^{4}+9r^{3}+14r^{2}+7r+2$$

Solution Steps

Combine 9r^{4} and 6r^{4} to get 15r^{4}.

$$15r^{4}+7r^{3}+7r^{2}+7r+2+2r^{3}+7r^{2}$$

Combine 7r^{3} and 2r^{3} to get 9r^{3}.

$$15r^{4}+9r^{3}+7r^{2}+7r+2+7r^{2}$$

Combine 7r^{2} and 7r^{2} to get 14r^{2}.

$$15r^{4}+9r^{3}+14r^{2}+7r+2$$

Differentiate w.r.t. r

$$60r^{3}+27r^{2}+28r+7$$