Solve 5xy/z^3*5yz/2x^5*5z/6yz

$$\frac { 5 x y } { z ^ { 3 } } \times \frac { 5 y z } { 2 x ^ { 5 } } \times \frac { 5 z } { 6 y z }$$

Evaluate

$$\frac{125y}{12z^{2}x^{4}}$$

Solution Steps

Cancel out z in both numerator and denominator.

$$\frac{5xy}{z^{3}}\times \frac{5yz}{2x^{5}}\times \frac{5}{6y}$$

Multiply \frac{5xy}{z^{3}} times \frac{5yz}{2x^{5}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5xy\times 5yz}{z^{3}\times 2x^{5}}\times \frac{5}{6y}$$

Cancel out xz in both numerator and denominator.

$$\frac{5\times 5yy}{2z^{2}x^{4}}\times \frac{5}{6y}$$

Multiply \frac{5\times 5yy}{2z^{2}x^{4}} times \frac{5}{6y} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 5yy\times 5}{2z^{2}x^{4}\times 6y}$$

Cancel out y in both numerator and denominator.

$$\frac{5\times 5\times 5y}{2\times 6z^{2}x^{4}}$$

Multiply 5 and 5 to get 25.

$$\frac{25\times 5y}{2\times 6z^{2}x^{4}}$$

Multiply 25 and 5 to get 125.

$$\frac{125y}{2\times 6z^{2}x^{4}}$$

Multiply 2 and 6 to get 12.

$$\frac{125y}{12z^{2}x^{4}}$$

Differentiate w.r.t. x

$$-\frac{125y}{3z^{2}x^{5}}$$