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

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

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

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

\frac{1}{y}

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

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

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

= \frac{1}{y} + 0

Simplify

= \frac{1}{y}

\int 3 x 3 - 3 x d x

\frac{d y}{d x} = \frac{2 x}{3 y ^{2}}

\frac{\partial}{\partial x} (e^{4 x y})

\frac{d}{d x} (x^{3} sin (2 x))

n = 1 \sum \infty \frac{( 3 ^{n + 1} )}{( 4 ^{n - 1} )}

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