Solve (7x^{8}-9x^{3}+2x^{2}+2)+(6x^6+2x^3-2x)+(-2x^3+7x^2+2x-1)

$$( 7 x ^ { 8 } - 9 x ^ { 3 } + 2 x ^ { 2 } + 2 ) + ( 6 x ^ { 6 } + 2 x ^ { 3 } - 2 x ) + ( - 2 x ^ { 3 } + 7 x ^ { 2 } + 2 x - 1 )$$

Evaluate

$$7x^{8}+6x^{6}-9x^{3}+9x^{2}+1$$

Solution Steps

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

$$7x^{8}-7x^{3}+2x^{2}+2+6x^{6}-2x-2x^{3}+7x^{2}+2x-1$$

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

$$7x^{8}-9x^{3}+2x^{2}+2+6x^{6}-2x+7x^{2}+2x-1$$

Combine 2x^{2} and 7x^{2} to get 9x^{2}.

$$7x^{8}-9x^{3}+9x^{2}+2+6x^{6}-2x+2x-1$$

Combine -2x and 2x to get 0.

$$7x^{8}-9x^{3}+9x^{2}+2+6x^{6}-1$$

Subtract 1 from 2 to get 1.

$$7x^{8}-9x^{3}+9x^{2}+1+6x^{6}$$

Differentiate w.r.t. x

$$x\left(56x^{6}+36x^{4}-27x+18\right)$$