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Popular >

derivative of f(x)=arctan(ln(x))

Solution

derivative of

f (x) = arctan (ln (x))

Solution

\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 )}

Graph

Popular Examples

integral of (32x^2)/((x-18)(x+6)^2)

\int \frac{32 x ^{2}}{( x - 18 ) ( x + 6 ) ^{2}} d x

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\frac{\partial}{\partial x} (2 x y z^{2} - 192)

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Frequently Asked Questions (FAQ)

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