Solve 4/3a^{3}bc-2/5ab^{2}c-a^3bc+ab^2c-1/3a^3bc+2/3ab^2c

$$\frac { 4 } { 3 } a ^ { 3 } b c - \frac { 2 } { 5 } a b ^ { 2 } c - a ^ { 3 } b c + a b ^ { 2 } c - \frac { 1 } { 3 } a ^ { 3 } b c + \frac { 2 } { 3 } a b ^ { 2 } c$$

Evaluate

$$\frac{19acb^{2}}{15}$$

Solution Steps

Multiply -1 and \frac{2}{5} to get -\frac{2}{5}.

$$\frac{4}{3}a^{3}bc-\frac{2}{5}ab^{2}c-a^{3}bc+ab^{2}c-\frac{1}{3}a^{3}bc+\frac{2}{3}ab^{2}c$$

Combine \frac{4}{3}a^{3}bc and -a^{3}bc to get \frac{1}{3}a^{3}bc.

$$\frac{1}{3}a^{3}bc-\frac{2}{5}ab^{2}c+ab^{2}c-\frac{1}{3}a^{3}bc+\frac{2}{3}ab^{2}c$$

Combine -\frac{2}{5}ab^{2}c and ab^{2}c to get \frac{3}{5}ab^{2}c.

$$\frac{1}{3}a^{3}bc+\frac{3}{5}ab^{2}c-\frac{1}{3}a^{3}bc+\frac{2}{3}ab^{2}c$$

Combine \frac{1}{3}a^{3}bc and -\frac{1}{3}a^{3}bc to get 0.

$$\frac{3}{5}ab^{2}c+\frac{2}{3}ab^{2}c$$

Combine \frac{3}{5}ab^{2}c and \frac{2}{3}ab^{2}c to get \frac{19}{15}ab^{2}c.

$$\frac{19}{15}ab^{2}c$$

Differentiate w.r.t. a

$$\frac{19cb^{2}}{15}$$