What is the derivative of arctan(ln(x)) ?

The derivative of arctan(ln(x)) is 1/(x(ln^2(x)+1))

What is the first derivative of arctan(ln(x)) ?

The first derivative of arctan(ln(x)) is 1/(x(ln^2(x)+1))

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\frac{d}{d x} (arctan (ln (x)))

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

Solution steps

\frac{d}{d x} (arctan (ln (x)))

Apply the chain rule:

\frac{1}{( ln ( x ) ) ^{2} + 1} \frac{d}{d x} (ln (x))

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

\frac{d}{d x} (ln (x)) = \frac{1}{x}

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

Simplify

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

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

What is the derivative of arctan(ln(x)) ?
The derivative of arctan(ln(x)) is 1/(x(ln^2(x)+1))
What is the first derivative of arctan(ln(x)) ?
The first derivative of arctan(ln(x)) is 1/(x(ln^2(x)+1))