Solve (5ab+[(-1/2ax)-(-3/2ax)]+[(-1/4ab)+(-3/2ab)]-ax

$$( 5 a b + [ ( - \frac { 1 } { 2 } a x ) - ( - \frac { 3 } { 2 } a x ) ] + [ ( - \frac { 1 } { 4 } a b ) + ( - \frac { 3 } { 2 } a b ) ] - a x$$

Evaluate

$$\frac{13ab}{4}$$

Solution Steps

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

$$5ab-\frac{1}{2}ax+\frac{3}{2}ax-\frac{1}{4}ab-\frac{3}{2}ab-ax$$

Combine -\frac{1}{2}ax and \frac{3}{2}ax to get ax.

$$5ab+ax-\frac{1}{4}ab-\frac{3}{2}ab-ax$$

Combine 5ab and -\frac{1}{4}ab to get \frac{19}{4}ab.

$$\frac{19}{4}ab+ax-\frac{3}{2}ab-ax$$

Combine \frac{19}{4}ab and -\frac{3}{2}ab to get \frac{13}{4}ab.

$$\frac{13}{4}ab+ax-ax$$

Combine ax and -ax to get 0.

$$\frac{13}{4}ab$$

Differentiate w.r.t. a

$$\frac{13b}{4}$$