Solve (-6c^{3}-5c^2-4c+1)+(7c^4-7c^3+2c^2+c-4)

$$( - 6 c ^ { 3 } - 5 c ^ { 2 } - 4 c + 1 ) + ( 7 c ^ { 4 } - 7 c ^ { 3 } + 2 c ^ { 2 } + c - 4 )$$

Evaluate

$$7c^{4}-13c^{3}-3c^{2}-3c-3$$

Solution Steps

Combine -6c^{3} and -7c^{3} to get -13c^{3}.

$$-13c^{3}-5c^{2}-4c+1+7c^{4}+2c^{2}+c-4$$

Combine -5c^{2} and 2c^{2} to get -3c^{2}.

$$-13c^{3}-3c^{2}-4c+1+7c^{4}+c-4$$

Combine -4c and c to get -3c.

$$-13c^{3}-3c^{2}-3c+1+7c^{4}-4$$

Subtract 4 from 1 to get -3.

$$-13c^{3}-3c^{2}-3c-3+7c^{4}$$

Differentiate w.r.t. c

$$28c^{3}-39c^{2}-6c-3$$