What is the derivative of f(x)=arctan(sqrt(x)) ?

The derivative of f(x)=arctan(sqrt(x)) is 1/(2sqrt(x)(x+1))

What is the first derivative of f(x)=arctan(sqrt(x)) ?

The first derivative of f(x)=arctan(sqrt(x)) is 1/(2sqrt(x)(x+1))

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derivative of

f (x) = arctan (x)

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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