What is (\partial}{\partial z}(\frac{(3x+y))/z) ?

The answer to (\partial}{\partial z}(\frac{(3x+y))/z) is -(3x+y)/(z^2)

Popular >

(\partial}{\partial z}(\frac{(3x+y))/z)

\frac{\partial}{\partial z} (\frac{( 3 x + y )}{z})

- \frac{3 x + y}{z ^{2}}

Solution steps

\frac{\partial}{\partial z} (\frac{( 3 x + y )}{z})

Treat

x, y

as constants

Take the constant out:

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

= (3 x + y) \frac{\partial}{\partial z} (\frac{1}{z})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= (3 x + y) \frac{\partial}{\partial z} (z^{- 1})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= (3 x + y) (- 1 \cdot z^{- 1 - 1})

Simplify

(3 x + y) (- 1 \cdot z^{- 1 - 1}) : - \frac{3 x + y}{z ^{2}}

= - \frac{3 x + y}{z ^{2}}

\frac{d y}{d t} = - y + 5

y^{^{''}} + 9 y^{^{'}} = 0, y (0) = 1, y^{^{'}} (0) = 1

\int \frac{y ^{2} - 9}{y} d y

9 x - x^{2}, 2 x, 0, 7

\frac{d}{d x} (4 - 4 x^{2})

What is (\partial}{\partial z}(\frac{(3x+y))/z) ?
The answer to (\partial}{\partial z}(\frac{(3x+y))/z) is -(3x+y)/(z^2)