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

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

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

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

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

Solution steps

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

Treat

z

as a constant

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

f (t) = t^{2} - t + 1

\frac{\partial}{\partial x} (\frac{y - x}{z})

\frac{d}{d x} ((x - 2) (x + 2))

t \frac{d y}{d t} - 3 y = \frac{4 t ^{5}}{t ^{2} + 4}

\int 11 sin^{3} (x co) s^{2} x d x

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