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

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

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

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

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

Solution steps

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

Treat

z, y

as constants

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (\frac{2 x + 4 x ^{2}}{( 1 + 4 x ) ^{2}})

x \to - 5 - lim (\frac{x}{x + 5})

(50, 43), (60, 86)

\frac{d y}{d x} = - 10 x y^{2}

\int_{0}^{\infty} e^{- 8 x} d x

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