What is (\partial}{\partial x}(\frac{x+y^2)/z) ?

The answer to (\partial}{\partial x}(\frac{x+y^2)/z) is 1/z

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(\partial}{\partial x}(\frac{x+y^2)/z)

\frac{\partial}{\partial x} (\frac{x + y ^{2}}{z})

\frac{1}{z}

Solution steps

\frac{\partial}{\partial x} (\frac{x + y ^{2}}{z})

Treat

y, z

as constants

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{z} \frac{\partial}{\partial x} (x + y^{2})

Apply the Sum/Difference Rule:

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

= \frac{1}{z} (\frac{\partial}{\partial x} (x) + \frac{\partial}{\partial x} (y^{2}))

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

\frac{\partial}{\partial x} (y^{2}) = 0

= \frac{1}{z} (1 + 0)

Simplify

= \frac{1}{z}

sin (x + 1)

t^{2} sin (t) \cdot e^{- 2 t}

\frac{d}{d x} ((1 + x y) e^{x y})

(3 x + 28)^{\frac{1}{2}}

\int e^{\frac{y}{x}} d y

What is (\partial}{\partial x}(\frac{x+y^2)/z) ?
The answer to (\partial}{\partial x}(\frac{x+y^2)/z) is 1/z