Solve 56x^3y^4/z^5*(-z^4/16{x^2{y}^6})

$$\frac{ 56 { x }^{ 3 } { y }^{ 4 } }{ { z }^{ 5 } } \times (- \frac{ { z }^{ 4 } }{ 16 { x }^{ 2 } { y }^{ 6 } } )$$

Evaluate

$$-\frac{7x}{2zy^{2}}$$

Solution Steps

Multiply \frac{56x^{3}y^{4}}{z^{5}} times -\frac{z^{4}}{16x^{2}y^{6}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-56x^{3}y^{4}z^{4}}{z^{5}\times 16x^{2}y^{6}}$$

Cancel out 8x^{2}y^{4}z^{4} in both numerator and denominator.

$$\frac{-7x}{2zy^{2}}$$

Differentiate w.r.t. x

$$-\frac{7}{2zy^{2}}$$