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

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

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

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

\frac{2}{z}

Solution steps

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

Treat

y, z

as constants

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (2 x) = 2

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

= \frac{1}{z} (2 + 0)

Simplify

\frac{1}{z} (2 + 0) : \frac{2}{z}

= \frac{2}{z}

\int cos (4 x) cos (5 x) d x

x^{2} + 6 x - 3

49 y^{^{''}} + 42 y^{^{'}} + 9 y = 0, y (0) = a, y^{^{'}} (0) = 2

x = \frac{( y - 3 ) ^{2}}{3}, y = 9 - x

7 x y \frac{d y}{d x} = 2

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