What is the derivative of 1/(arctan(x^2)) ?

The derivative of 1/(arctan(x^2)) is -(2x)/(arctan^2(x^2)(x^4+1))

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

The first derivative of 1/(arctan(x^2)) is -(2x)/(arctan^2(x^2)(x^4+1))

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

- \frac{2 x}{arctan ^{2} ( x ^{2} ) ( x ^{4} + 1 )}

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (arctan (x^{2})) = \frac{2 x}{x ^{4} + 1}

= - \frac{1}{( arctan ( x ^{2} ) ) ^{2}} \cdot \frac{2 x}{x ^{4} + 1}

Simplify

- \frac{1}{arctan ^{2} ( x ^{2} )} \cdot \frac{2 x}{x ^{4} + 1} : - \frac{2 x}{arctan ^{2} ( x ^{2} ) ( x ^{4} + 1 )}

= - \frac{2 x}{arctan ^{2} ( x ^{2} ) ( x ^{4} + 1 )}

\int cos^{2} (x) d x

(1 + cos (t)) \frac{d y}{d t} = (1 + e^{- y}) sin (t)

\frac{d}{d x} ((\frac{2 x + 1}{3 x - 1})^{4})

\frac{d}{d x} (8 x^{2} cos (x) cot (x))

x \cdot e^{- x + 1}

What is the derivative of 1/(arctan(x^2)) ?
The derivative of 1/(arctan(x^2)) is -(2x)/(arctan^2(x^2)(x^4+1))
What is the first derivative of 1/(arctan(x^2)) ?
The first derivative of 1/(arctan(x^2)) is -(2x)/(arctan^2(x^2)(x^4+1))