What is (\partial)/(\partial x)(4x(5+y)^{-1}) ?

The answer to (\partial)/(\partial x)(4x(5+y)^{-1}) is 4/(5+y)

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(\partial)/(\partial x)(4x(5+y)^{-1})

\frac{\partial}{\partial x} (4 x (5 + y)^{- 1})

\frac{4}{5 + y}

Solution steps

\frac{\partial}{\partial x} (4 x (5 + y)^{- 1})

Treat

y

as a constant

Take the constant out:

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

= 4 (5 + y)^{- 1} \frac{\partial}{\partial x} (x)

Apply the common derivative:

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

= 4 (5 + y)^{- 1} \cdot 1

Simplify

4 (5 + y)^{- 1} \cdot 1 : \frac{4}{5 + y}

= \frac{4}{5 + y}

What is (\partial)/(\partial x)(4x(5+y)^{-1}) ?
The answer to (\partial)/(\partial x)(4x(5+y)^{-1}) is 4/(5+y)