Solve (-1/14mn^2+6/7mn^2)+(-8/7mn)*n-mn^2*(-3/14)

$$( - \frac { 1 } { 14 } m n ^ { 2 } + \frac { 6 } { 7 } m n ^ { 2 } ) + ( - \frac { 8 } { 7 } m n ) \cdot n - m n ^ { 2 } \cdot ( - \frac { 3 } { 14 } )$$

Evaluate

$$-\frac{mn^{2}}{7}$$

Solution Steps

Multiply n and n to get n^{2}.

$$-\frac{1}{14}mn^{2}+\frac{6}{7}mn^{2}-\frac{8}{7}mn^{2}-mn^{2}\left(-\frac{3}{14}\right)$$

Combine -\frac{1}{14}mn^{2} and \frac{6}{7}mn^{2} to get \frac{11}{14}mn^{2}.

$$\frac{11}{14}mn^{2}-\frac{8}{7}mn^{2}-mn^{2}\left(-\frac{3}{14}\right)$$

Combine \frac{11}{14}mn^{2} and -\frac{8}{7}mn^{2} to get -\frac{5}{14}mn^{2}.

$$-\frac{5}{14}mn^{2}-mn^{2}\left(-\frac{3}{14}\right)$$

Combine -\frac{5}{14}mn^{2} and -mn^{2}\left(-\frac{3}{14}\right) to get -\frac{1}{7}mn^{2}.

$$-\frac{1}{7}mn^{2}$$

Differentiate w.r.t. m

$$-\frac{n^{2}}{7}$$