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

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

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(\partial)/(\partial x)((2y)/(x+z))

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

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

Solution steps

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

Treat

y, z

as constants

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int (1 - x)^{5} d x

n = 1 \sum \infty 8 \cdot (\frac{1}{3})^{n}

\frac{d}{d x} (\frac{( x ^{2} - 5 x ) ^{2}}{( 6 x + 7 ) ^{3}})

(- 5, 5), (- 7, 5)

\frac{d}{d x} (\frac{5 x ^{2} - 15}{3 ( x ^{2} - 5 ) ^{\frac{2}{3}}})

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