Solve 5acd/3mnp*3mn/ac*-1/m^2n^2*m^2n^2*m/n

$$\frac { 5 a c d } { 3 m n p } \cdot \frac { 3 m n } { a c } \cdot \frac { - 1 } { m ^ { 2 } n ^ { 2 } } \cdot m ^ { 2 } n ^ { 2 } \cdot \frac { m } { n }$$

Evaluate

$$-\frac{5dm}{np}$$

Solution Steps

Multiply \frac{5acd}{3mnp} times \frac{3mn}{ac} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5acd\times 3mn}{3mnpac}\times \frac{-1}{m^{2}n^{2}}m^{2}n^{2}\times \frac{m}{n}$$

Cancel out 3acmn in both numerator and denominator.

$$\frac{5d}{p}\times \frac{-1}{m^{2}n^{2}}m^{2}n^{2}\times \frac{m}{n}$$

Multiply \frac{5d}{p} times \frac{-1}{m^{2}n^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5d\left(-1\right)}{pm^{2}n^{2}}m^{2}n^{2}\times \frac{m}{n}$$

Express \frac{5d\left(-1\right)}{pm^{2}n^{2}}m^{2} as a single fraction.

$$\frac{5d\left(-1\right)m^{2}}{pm^{2}n^{2}}n^{2}\times \frac{m}{n}$$

Cancel out m^{2} in both numerator and denominator.

$$\frac{-5d}{pn^{2}}n^{2}\times \frac{m}{n}$$

Express \frac{-5d}{pn^{2}}n^{2} as a single fraction.

$$\frac{-5dn^{2}}{pn^{2}}\times \frac{m}{n}$$

Cancel out n^{2} in both numerator and denominator.

$$\frac{-5d}{p}\times \frac{m}{n}$$

Multiply \frac{-5d}{p} times \frac{m}{n} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-5dm}{pn}$$

Differentiate w.r.t. m

$$-\frac{5d}{np}$$