Solve 3xy/z^4*4yz/3x^7*5z/6yz

$$\frac { 3 x y } { z ^ { 4 } } \times \frac { 4 y z } { 3 x ^ { 7 } } \times \frac { 5 z } { 6 y z }$$

Evaluate

$$\frac{10y}{3z^{3}x^{6}}$$

Solution Steps

Cancel out z in both numerator and denominator.

$$\frac{3xy}{z^{4}}\times \frac{4yz}{3x^{7}}\times \frac{5}{6y}$$

Multiply \frac{3xy}{z^{4}} times \frac{4yz}{3x^{7}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3xy\times 4yz}{z^{4}\times 3x^{7}}\times \frac{5}{6y}$$

Cancel out 3xz in both numerator and denominator.

$$\frac{4yy}{z^{3}x^{6}}\times \frac{5}{6y}$$

Multiply \frac{4yy}{z^{3}x^{6}} times \frac{5}{6y} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4yy\times 5}{z^{3}x^{6}\times 6y}$$

Cancel out 2y in both numerator and denominator.

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

Multiply 2 and 5 to get 10.

$$\frac{10y}{3z^{3}x^{6}}$$

Differentiate w.r.t. x

$$-\frac{20y}{z^{3}x^{7}}$$