Solve xy/z^3/frac{x^6{y^5z}}

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

Evaluate

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

Solution Steps

Divide \frac{xy}{z^{3}} by \frac{x^{6}}{y^{5}z} by multiplying \frac{xy}{z^{3}} by the reciprocal of \frac{x^{6}}{y^{5}z}.

$$\frac{xyy^{5}z}{z^{3}x^{6}}$$

Cancel out xz in both numerator and denominator.

$$\frac{yy^{5}}{z^{2}x^{5}}$$

To multiply powers of the same base, add their exponents. Add 1 and 5 to get 6.

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

Differentiate w.r.t. x

$$-\frac{5\times \left(\frac{y}{x}\right)^{6}}{z^{2}}$$