What is (\partial)/(\partial x)(nln(x/2)) ?

The answer to (\partial)/(\partial x)(nln(x/2)) is n/x

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(\partial)/(\partial x)(nln(x/2))

\frac{\partial}{\partial x} (n ln (\frac{x}{2}))

\frac{n}{x}

Solution steps

\frac{\partial}{\partial x} (n ln (\frac{x}{2}))

Take the constant out:

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

= n \frac{\partial}{\partial x} (ln (\frac{x}{2}))

Apply the chain rule:

\frac{1}{\frac{x}{2}} \frac{\partial}{\partial x} (\frac{x}{2})

= \frac{1}{\frac{x}{2}} \frac{\partial}{\partial x} (\frac{x}{2})

\frac{\partial}{\partial x} (\frac{x}{2}) = \frac{1}{2}

= n \frac{1}{\frac{x}{2}} \cdot \frac{1}{2}

Simplify

n \frac{1}{\frac{x}{2}} \cdot \frac{1}{2} : \frac{n}{x}

= \frac{n}{x}

g (t) = \frac{7}{8 t ^{4}}

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\frac{\partial}{\partial x} (z (1 + e^{x + y}))

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What is (\partial)/(\partial x)(nln(x/2)) ?
The answer to (\partial)/(\partial x)(nln(x/2)) is n/x