Solve -2xy^4/9z^5*-3z/3x^3y^3

$$\frac { - 2 x y ^ { 4 } } { 9 z ^ { 5 } } \cdot \frac { - 3 z } { 3 x ^ { 3 } y ^ { 3 } }$$

Evaluate

$$\frac{2y}{9x^{2}z^{4}}$$

Solution Steps

Cancel out 3 in both numerator and denominator.

$$\frac{-2xy^{4}}{9z^{5}}\times \frac{-z}{x^{3}y^{3}}$$

Multiply \frac{-2xy^{4}}{9z^{5}} times \frac{-z}{x^{3}y^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-2xy^{4}\left(-1\right)z}{9z^{5}x^{3}y^{3}}$$

Cancel out xzy^{3} in both numerator and denominator.

$$\frac{-2\left(-1\right)y}{9x^{2}z^{4}}$$

Multiply -2 and -1 to get 2.

$$\frac{2y}{9x^{2}z^{4}}$$

Differentiate w.r.t. x

$$-\frac{4y}{9x^{3}z^{4}}$$