Solve (7x^{4}-5x^{5}+4x^{2}-7)+(x^3-3x^2-5+x)+(-3x^4+5-8x+2x^3)

$$( 7 x ^ { 4 } - 5 x ^ { 5 } + 4 x ^ { 2 } - 7 ) + ( x ^ { 3 } - 3 x ^ { 2 } - 5 + x ) + ( - 3 x ^ { 4 } + 5 - 8 x + 2 x ^ { 3 } )$$

Evaluate

$$-5x^{5}+4x^{4}+3x^{3}+x^{2}-7x-7$$

Solution Steps

Combine 4x^{2} and -3x^{2} to get x^{2}.

$$7x^{4}-5x^{5}+x^{2}-7+x^{3}-5+x-3x^{4}+5-8x+2x^{3}$$

Subtract 5 from -7 to get -12.

$$7x^{4}-5x^{5}+x^{2}-12+x^{3}+x-3x^{4}+5-8x+2x^{3}$$

Combine 7x^{4} and -3x^{4} to get 4x^{4}.

$$4x^{4}-5x^{5}+x^{2}-12+x^{3}+x+5-8x+2x^{3}$$

Add -12 and 5 to get -7.

$$4x^{4}-5x^{5}+x^{2}-7+x^{3}+x-8x+2x^{3}$$

Combine x and -8x to get -7x.

$$4x^{4}-5x^{5}+x^{2}-7+x^{3}-7x+2x^{3}$$

Combine x^{3} and 2x^{3} to get 3x^{3}.

$$4x^{4}-5x^{5}+x^{2}-7+3x^{3}-7x$$

Differentiate w.r.t. x

$$-25x^{4}+16x^{3}+9x^{2}+2x-7$$