Solve (-1/2a^{3}xy)-(1/3a^{3}xy)-(4/9a^{2}x^2)+(5/6a^3xy)-(-frac{5}{9}a^2x^2)

$$( - \frac { 1 } { 2 } a ^ { 3 } x y ) - ( \frac { 1 } { 3 } a ^ { 3 } x y ) - ( \frac { 4 } { 9 } a ^ { 2 } x ^ { 2 } ) + ( \frac { 5 } { 6 } a ^ { 3 } x y ) - ( - \frac { 5 } { 9 } a ^ { 2 } x ^ { 2 } )$$

Evaluate

$$\frac{\left(ax\right)^{2}}{9}$$

Solution Steps

Combine -\frac{1}{2}a^{3}xy and -\frac{1}{3}a^{3}xy to get -\frac{5}{6}a^{3}xy.

$$-\frac{5}{6}a^{3}xy-\frac{4}{9}a^{2}x^{2}+\frac{5}{6}a^{3}xy-\left(-\frac{5}{9}a^{2}x^{2}\right)$$

The opposite of -\frac{5}{9}a^{2}x^{2} is \frac{5}{9}a^{2}x^{2}.

$$-\frac{5}{6}a^{3}xy-\frac{4}{9}a^{2}x^{2}+\frac{5}{6}a^{3}xy+\frac{5}{9}a^{2}x^{2}$$

Combine -\frac{5}{6}a^{3}xy and \frac{5}{6}a^{3}xy to get 0.

$$-\frac{4}{9}a^{2}x^{2}+\frac{5}{9}a^{2}x^{2}$$

Combine -\frac{4}{9}a^{2}x^{2} and \frac{5}{9}a^{2}x^{2} to get \frac{1}{9}a^{2}x^{2}.

$$\frac{1}{9}a^{2}x^{2}$$

Differentiate w.r.t. x

$$\frac{2xa^{2}}{9}$$