What is (\partial)/(\partial z)(-1/((y+2z)^2)) ?

The answer to (\partial)/(\partial z)(-1/((y+2z)^2)) is 4/((y+2z)^3)

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(\partial)/(\partial z)(-1/((y+2z)^2))

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

\frac{4}{( y + 2 z ) ^{3}}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

- \frac{2}{( y + 2 z ) ^{3}} \frac{\partial}{\partial z} (y + 2 z)

= - \frac{2}{( y + 2 z ) ^{3}} \frac{\partial}{\partial z} (y + 2 z)

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

= - (- \frac{2}{( y + 2 z ) ^{3}} \cdot 2)

Simplify

- (- \frac{2}{( y + 2 z ) ^{3}} \cdot 2) : \frac{4}{( y + 2 z ) ^{3}}

= \frac{4}{( y + 2 z ) ^{3}}

\int \frac{3 e ^{2 x}}{1 + e ^{2 x}} d x

f (x) = sin (2 x), 0, \frac{π}{2}

\frac{d}{d x} (5 sin (x) + 3 cos (x))

\frac{d}{d x} (e^{- x y})

ln (4 + x)

What is (\partial)/(\partial z)(-1/((y+2z)^2)) ?
The answer to (\partial)/(\partial z)(-1/((y+2z)^2)) is 4/((y+2z)^3)