Solve frac{5x^{2}}{7y^3}*4y^2/7n^3*14m/5x^4

$$\frac { 5 x ^ { 2 } } { 7 y ^ { 3 } } \times \frac { 4 y ^ { 2 } } { 7 n ^ { 3 } } \times \frac { 14 m } { 5 x ^ { 4 } }$$

Evaluate

$$\frac{8m}{7yx^{2}n^{3}}$$

Solution Steps

Multiply \frac{5x^{2}}{7y^{3}} times \frac{4y^{2}}{7n^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5x^{2}\times 4y^{2}}{7y^{3}\times 7n^{3}}\times \frac{14m}{5x^{4}}$$

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

$$\frac{4\times 5x^{2}}{7\times 7yn^{3}}\times \frac{14m}{5x^{4}}$$

Multiply \frac{4\times 5x^{2}}{7\times 7yn^{3}} times \frac{14m}{5x^{4}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 5x^{2}\times 14m}{7\times 7yn^{3}\times 5x^{4}}$$

Cancel out 5\times 7x^{2} in both numerator and denominator.

$$\frac{2\times 4m}{7yx^{2}n^{3}}$$

Multiply 2 and 4 to get 8.

$$\frac{8m}{7yx^{2}n^{3}}$$

Differentiate w.r.t. x

$$-\frac{16m}{7y\left(nx\right)^{3}}$$