Solve -x^2-y^2-z^2-3x^2-4{y}^2+5{z}^2+4{x}^2=

$$- { x }^{ 2 } - { y }^{ 2 } - { z }^{ 2 } -3 { x }^{ 2 } -4 { y }^{ 2 } +5 { z }^{ 2 } +4 { x }^{ 2 } =$$

Evaluate

$$4z^{2}-5y^{2}$$

Solution Steps

Combine -y^{2} and -4y^{2} to get -5y^{2}.

$$-x^{2}-5y^{2}-z^{2}-3x^{2}+5z^{2}+4x^{2}$$

Combine -z^{2} and 5z^{2} to get 4z^{2}.

$$-x^{2}-5y^{2}+4z^{2}-3x^{2}+4x^{2}$$

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

$$-x^{2}-5y^{2}+4z^{2}+x^{2}$$

Combine -x^{2} and x^{2} to get 0.

$$-5y^{2}+4z^{2}$$

Differentiate w.r.t. y

$$-10y$$