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

The answer to (\partial)/(\partial y)(x+y/z) is 1/z

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

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

\frac{1}{z}

Solution steps

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

Treat

x, z

as constants

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial y} (\frac{y}{z}) = \frac{1}{z}

= 0 + \frac{1}{z}

Simplify

= \frac{1}{z}

\int 7 x e^{6 x} d x

y = 2 x^{2} + 1, (3, 19)

f (x) = (1 + 2 x)^{2}, at x = 4

\frac{x ^{3}}{2 - x ^{2}}

(sin^{4} (x))^{^{'}}

What is (\partial)/(\partial y)(x+y/z) ?
The answer to (\partial)/(\partial y)(x+y/z) is 1/z