Solve 7y/6x^21/9xy5x/12y^3=

$$\frac { 7 y } { 6 x ^ { 2 } } \frac { 1 } { 9 x y } \frac { 5 x } { 12 y ^ { 3 } } =$$

Evaluate

$$\frac{35}{648x^{2}y^{3}}$$

Solution Steps

Multiply \frac{7y}{6x^{2}} times \frac{1}{9xy} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7y}{6x^{2}\times 9xy}\times \frac{5x}{12y^{3}}$$

Cancel out y in both numerator and denominator.

$$\frac{7}{6\times 9xx^{2}}\times \frac{5x}{12y^{3}}$$

Multiply \frac{7}{6\times 9xx^{2}} times \frac{5x}{12y^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 5x}{6\times 9xx^{2}\times 12y^{3}}$$

Cancel out x in both numerator and denominator.

$$\frac{5\times 7}{6\times 9\times 12x^{2}y^{3}}$$

Multiply 5 and 7 to get 35.

$$\frac{35}{6\times 9\times 12x^{2}y^{3}}$$

Multiply 6 and 9 to get 54.

$$\frac{35}{54\times 12x^{2}y^{3}}$$

Multiply 54 and 12 to get 648.

$$\frac{35}{648x^{2}y^{3}}$$

Differentiate w.r.t. x

$$-\frac{35}{324\left(xy\right)^{3}}$$