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

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

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

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

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

Solution steps

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

Treat

x, y

as constants

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x^{^{''}} + 4 x = 0

n = 1 \sum \infty \frac{1}{n + 1 ^{- n}}

5 y^{^{''}} + 15 y^{^{'}} - 20 y = 0

\int (x^{2} - x + 1) d x

\int \frac{6}{x ^{2} x ^{2} + 16} d x

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