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Popular >

derivative of arctan(sqrt(x+1))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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\int \frac{x ^{2}}{x ^{3}} + 5 d x

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Frequently Asked Questions (FAQ)

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