What is (\partial)/(\partial z)(x/y+y/z) ?

The answer to (\partial)/(\partial z)(x/y+y/z) is -y/(z^2)

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(\partial)/(\partial z)(x/y+y/z)

\frac{\partial}{\partial z} (\frac{x}{y} + \frac{y}{z})

- \frac{y}{z ^{2}}

Solution steps

\frac{\partial}{\partial z} (\frac{x}{y} + \frac{y}{z})

Treat

x, y

as constants

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial z} (\frac{x}{y}) + \frac{\partial}{\partial z} (\frac{y}{z})

\frac{\partial}{\partial z} (\frac{x}{y}) = 0

\frac{\partial}{\partial z} (\frac{y}{z}) = - \frac{y}{z ^{2}}

= 0 - \frac{y}{z ^{2}}

Simplify

= - \frac{y}{z ^{2}}

y^{^{''}} + 6 y^{^{'}} + 25 y = 0, y (0) = 3, y^{^{'}} (0) = - 8

2 y^{3} d x + 3 y^{2} d y = 0

\int \frac{1}{k x - n x ^{2}} d x

(1.4) (- 5)

\int 6 \frac{sin ( 2 x )}{sin ( x )} d x

What is (\partial)/(\partial z)(x/y+y/z) ?
The answer to (\partial)/(\partial z)(x/y+y/z) is -y/(z^2)