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Popular >

derivative of y=sqrt(arctan(x))

Solution

derivative of

y = arctan (x)

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

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(\partial)/(\partial x)(e^{2xy^2}+3x)

\frac{\partial}{\partial x} (e^{2 x y^{2}} + 3 x)

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\frac{d}{d x} (\frac{3 ^{x}}{tan ( x )})

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y = \frac{x ^{7}}{f ( x )}

Frequently Asked Questions (FAQ)

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