What is the derivative of 1/(arctan(x)) ?

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

What is the first derivative of 1/(arctan(x)) ?

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

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derivative of

\frac{1}{arctan ( x )}

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int (x^{2} + 5)^{3} x d x

\int x (x^{2} - 1)^{99} d x

n = 0 \sum \infty \frac{1}{n + 9}

\int x^{3} + 3 d x

\frac{d y}{d x} = 2 x - y, y (0) = 1

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