Solve (-10t^{5}+9t^{4}-3t^3+2t+11)+(-6-3t-3t^2+3t^3+3t^5)

$$( - 10 t ^ { 5 } + 9 t ^ { 4 } - 3 t ^ { 3 } + 2 t + 11 ) + ( - 6 - 3 t - 3 t ^ { 2 } + 3 t ^ { 3 } + 3 t ^ { 5 } )$$

Evaluate

$$5-t-3t^{2}+9t^{4}-7t^{5}$$

Solution Steps

Subtract 6 from 11 to get 5.

$$-10t^{5}+9t^{4}-3t^{3}+2t+5-3t-3t^{2}+3t^{3}+3t^{5}$$

Combine 2t and -3t to get -t.

$$-10t^{5}+9t^{4}-3t^{3}-t+5-3t^{2}+3t^{3}+3t^{5}$$

Combine -3t^{3} and 3t^{3} to get 0.

$$-10t^{5}+9t^{4}-t+5-3t^{2}+3t^{5}$$

Combine -10t^{5} and 3t^{5} to get -7t^{5}.

$$-7t^{5}+9t^{4}-t+5-3t^{2}$$

Differentiate w.r.t. t

$$-35t^{4}+36t^{3}-6t-1$$