Solve 7x^2+3xy+6y^2+-5x^3+5xy+6x^2-{y}^{2}-7{x}^2+3xy+6{y}^2-6{x}^3+4xy-2{y}^2+x2

$$7 { x }^{ 2 } +3xy+6 { y }^{ 2 } +-5 { x }^{ 3 } +5xy+6 { x }^{ 2 } - { y }^{ 2 } -7 { x }^{ 2 } +3xy+6 { y }^{ 2 } -6 { x }^{ 3 } +4xy-2 { y }^{ 2 } +x2$$

Evaluate

$$9y^{2}+x_{2}+15xy+6x^{2}-11x^{3}$$

Solution Steps

Combine 3xy and 5xy to get 8xy.

$$7x^{2}+8xy+6y^{2}-5x^{3}+6x^{2}-y^{2}-7x^{2}+3xy+6y^{2}-6x^{3}+4xy-2y^{2}+x_{2}$$

Combine 7x^{2} and 6x^{2} to get 13x^{2}.

$$13x^{2}+8xy+6y^{2}-5x^{3}-y^{2}-7x^{2}+3xy+6y^{2}-6x^{3}+4xy-2y^{2}+x_{2}$$

Combine 6y^{2} and -y^{2} to get 5y^{2}.

$$13x^{2}+8xy+5y^{2}-5x^{3}-7x^{2}+3xy+6y^{2}-6x^{3}+4xy-2y^{2}+x_{2}$$

Combine 13x^{2} and -7x^{2} to get 6x^{2}.

$$6x^{2}+8xy+5y^{2}-5x^{3}+3xy+6y^{2}-6x^{3}+4xy-2y^{2}+x_{2}$$

Combine 8xy and 3xy to get 11xy.

$$6x^{2}+11xy+5y^{2}-5x^{3}+6y^{2}-6x^{3}+4xy-2y^{2}+x_{2}$$

Combine 5y^{2} and 6y^{2} to get 11y^{2}.

$$6x^{2}+11xy+11y^{2}-5x^{3}-6x^{3}+4xy-2y^{2}+x_{2}$$

Combine -5x^{3} and -6x^{3} to get -11x^{3}.

$$6x^{2}+11xy+11y^{2}-11x^{3}+4xy-2y^{2}+x_{2}$$

Combine 11xy and 4xy to get 15xy.

$$6x^{2}+15xy+11y^{2}-11x^{3}-2y^{2}+x_{2}$$

Combine 11y^{2} and -2y^{2} to get 9y^{2}.

$$6x^{2}+15xy+9y^{2}-11x^{3}+x_{2}$$

Differentiate w.r.t. x

$$15y+12x-33x^{2}$$