Solve 1/3xy^2-1/2xy^2+1/3x^2y+1/2x^2y+frac{1}{6}x{y}^2+frac{1}{6}{x}^2y

$$\frac{ 1 }{ 3 } x { y }^{ 2 } - \frac{ 1 }{ 2 } x { y }^{ 2 } + \frac{ 1 }{ 3 } { x }^{ 2 } y+ \frac{ 1 }{ 2 } { x }^{ 2 } y+ \frac{ 1 }{ 6 } x { y }^{ 2 } + \frac{ 1 }{ 6 } { x }^{ 2 } y$$

Evaluate

$$yx^{2}$$

Solution Steps

Combine \frac{1}{3}xy^{2} and -\frac{1}{2}xy^{2} to get -\frac{1}{6}xy^{2}.

$$-\frac{1}{6}xy^{2}+\frac{1}{3}x^{2}y+\frac{1}{2}x^{2}y+\frac{1}{6}xy^{2}+\frac{1}{6}x^{2}y$$

Combine \frac{1}{3}x^{2}y and \frac{1}{2}x^{2}y to get \frac{5}{6}x^{2}y.

$$-\frac{1}{6}xy^{2}+\frac{5}{6}x^{2}y+\frac{1}{6}xy^{2}+\frac{1}{6}x^{2}y$$

Combine -\frac{1}{6}xy^{2} and \frac{1}{6}xy^{2} to get 0.

$$\frac{5}{6}x^{2}y+\frac{1}{6}x^{2}y$$

Combine \frac{5}{6}x^{2}y and \frac{1}{6}x^{2}y to get x^{2}y.

$$x^{2}y$$

Differentiate w.r.t. x

$$2xy$$