What is (\partial)/(\partial x)(1/(ln(x/2))) ?

The answer to (\partial)/(\partial x)(1/(ln(x/2))) is -1/(xln^2(x/2))

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(\partial)/(\partial x)(1/(ln(x/2)))

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

- \frac{1}{x ln ^{2} ( \frac{x}{2} )}

Solution steps

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

Apply exponent rule:

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

= \frac{\partial}{\partial x} (ln^{- 1} (\frac{x}{2}))

Apply the chain rule:

- \frac{1}{( ln ( \frac{x}{2} ) ) ^{2}} \frac{\partial}{\partial x} (ln (\frac{x}{2}))

= - \frac{1}{( ln ( \frac{x}{2} ) ) ^{2}} \frac{\partial}{\partial x} (ln (\frac{x}{2}))

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

= - \frac{1}{( ln ( \frac{x}{2} ) ) ^{2}} \cdot \frac{1}{x}

Simplify

- \frac{1}{ln ^{2} ( \frac{x}{2} )} \cdot \frac{1}{x} : - \frac{1}{x ln ^{2} ( \frac{x}{2} )}

= - \frac{1}{x ln ^{2} ( \frac{x}{2} )}

y = e^{5 x}, at x = \frac{1}{5} ln (3)

(- 2 sin (x))^{^{'}}

x^{3} + \frac{1}{x ^{3}}

ln (x + 2)

\int ln (x) ln (x) d x

What is (\partial)/(\partial x)(1/(ln(x/2))) ?
The answer to (\partial)/(\partial x)(1/(ln(x/2))) is -1/(xln^2(x/2))