Solve (2abc^2-1/2abc^2-3/2abc^2+1/4abc^2)

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

Evaluate

$$\frac{abc^{2}}{4}$$

Solution Steps

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

$$\frac{3}{2}abc^{2}-\frac{3}{2}abc^{2}+\frac{1}{4}abc^{2}$$

Combine \frac{3}{2}abc^{2} and -\frac{3}{2}abc^{2} to get 0.

$$0+\frac{1}{4}abc^{2}$$

Anything plus zero gives itself.

$$\frac{1}{4}abc^{2}$$

Differentiate w.r.t. a

$$\frac{bc^{2}}{4}$$