Solve -(-2/3xy^{2})+1/3xy^2-1/3x^2y+xy^2-(-1/3x^2y)

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

Evaluate

$$2xy^{2}$$

Solution Steps

The opposite of -\frac{2}{3}xy^{2} is \frac{2}{3}xy^{2}.

$$\frac{2}{3}xy^{2}+\frac{1}{3}xy^{2}-\frac{1}{3}x^{2}y+xy^{2}-\left(-\frac{1}{3}x^{2}y\right)$$

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

$$xy^{2}-\frac{1}{3}x^{2}y+xy^{2}-\left(-\frac{1}{3}x^{2}y\right)$$

The opposite of -\frac{1}{3}x^{2}y is \frac{1}{3}x^{2}y.

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

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

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

Combine -\frac{1}{3}x^{2}y and \frac{1}{3}x^{2}y to get 0.

$$2xy^{2}$$

Differentiate w.r.t. x

$$2y^{2}$$