Solve (5/9ab^2-1/2ab^2-4/3ab^2)

$$( \frac { 5 } { 9 } a b ^ { 2 } - \frac { 1 } { 2 } a b ^ { 2 } - \frac { 4 } { 3 } a b ^ { 2 } )$$

Evaluate

$$-\frac{23ab^{2}}{18}$$

Solution Steps

Combine \frac{5}{9}ab^{2} and -\frac{1}{2}ab^{2} to get \frac{1}{18}ab^{2}.

$$\frac{1}{18}ab^{2}-\frac{4}{3}ab^{2}$$

Combine \frac{1}{18}ab^{2} and -\frac{4}{3}ab^{2} to get -\frac{23}{18}ab^{2}.

$$-\frac{23}{18}ab^{2}$$

Differentiate w.r.t. a

$$-\frac{23b^{2}}{18}$$