Solve 1/6xy+1/9xy+1/2xy+1/2xy-frac{1}{2}xy+frac{1}{3}xy

$$\frac { 1 } { 6 } x y + \frac { 1 } { 9 } x y + \frac { 1 } { 2 } x y + \frac { 1 } { 2 } x y - \frac { 1 } { 2 } x y + \frac { 1 } { 3 } x y$$

Evaluate

$$\frac{10xy}{9}$$

Solution Steps

Combine \frac{1}{6}xy and \frac{1}{9}xy to get \frac{5}{18}xy.

$$\frac{5}{18}xy+\frac{1}{2}xy+\frac{1}{2}xy-\frac{1}{2}xy+\frac{1}{3}xy$$

Combine \frac{5}{18}xy and \frac{1}{2}xy to get \frac{7}{9}xy.

$$\frac{7}{9}xy+\frac{1}{2}xy-\frac{1}{2}xy+\frac{1}{3}xy$$

Combine \frac{7}{9}xy and \frac{1}{2}xy to get \frac{23}{18}xy.

$$\frac{23}{18}xy-\frac{1}{2}xy+\frac{1}{3}xy$$

Combine \frac{23}{18}xy and -\frac{1}{2}xy to get \frac{7}{9}xy.

$$\frac{7}{9}xy+\frac{1}{3}xy$$

Combine \frac{7}{9}xy and \frac{1}{3}xy to get \frac{10}{9}xy.

$$\frac{10}{9}xy$$

Differentiate w.r.t. x

$$\frac{10y}{9}$$