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Popular >

derivative of ln(arctan(x))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

\frac{1}{arctan ( x )} \frac{d}{d x} (arctan (x))

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

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

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

Simplify

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

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

Popular Examples

\frac{d y}{d x} - 3 y = 0

sum from n=1 to infinity of (-0.7)^{n-1}

n = 1 \sum \infty (- 0.7)^{n - 1}

(\partial)/(\partial t)(x/t)

\frac{\partial}{\partial t} (\frac{x}{t})

integral from 0 to 3 of pi(9x^2-x^4)

\int_{0}^{3} π (9 x^{2} - x^{4}) d x

limit as x approaches 1 of e^{6x^5-6x}

x \to 1 lim (e^{6 x^{5} - 6 x})

Frequently Asked Questions (FAQ)

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