Solve 1+x^2+x^4+x^6+x^8+{x}^9div1+{x}^2+{x}^4

$$1+ { x }^{ 2 } + { x }^{ 4 } + { x }^{ 6 } + { x }^{ 8 } + { x }^{ 9 } \div 1+ { x }^{ 2 } + { x }^{ 4 }$$

Evaluate

$$x^{9}+\left(x^{4}+1\right)^{2}+x^{6}+2x^{2}$$

Solution Steps

Anything divided by one gives itself.

$$1+x^{2}+x^{4}+x^{6}+x^{8}+x^{9}+x^{2}+x^{4}$$

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

$$1+2x^{2}+x^{4}+x^{6}+x^{8}+x^{9}+x^{4}$$

Combine x^{4} and x^{4} to get 2x^{4}.

$$1+2x^{2}+2x^{4}+x^{6}+x^{8}+x^{9}$$

Differentiate w.r.t. x

$$x\left(9x^{7}+8x^{2}\left(x^{4}+1\right)+6x^{4}+4\right)$$