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Popular >

derivative of y=(arctan(x))^2

Solution

derivative of

y = (arctan (x))^{2}

Solution

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

Solution steps

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

Apply the chain rule:

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

= 2 arctan (x) \frac{d}{d x} (arctan (x))

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

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

Simplify

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

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

Popular Examples

derivative of sqrt(x^2-16)

\frac{d}{d x} (x^{2} - 16)

integral from-ln(4) to 0 of 6sqrt(3)e^t

\int_{- l n (4)}^{0} 63 e^{t} d t

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\frac{d}{d x} (\frac{e ^{x}}{x + 2})

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f (x) = (2 x^{2} - 4)^{4}

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

Frequently Asked Questions (FAQ)

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