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

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

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

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

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derivative of

y = 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 )}

\int 3 x - 4 d x

\int_{0}^{1} (3 x - 2)^{2} d x

y = x^{2} + x, (2, - 3)

f^{^{'}} (x) = x^{3} (x^{4} - 1)

x \to 0 lim (\frac{1}{1 + 5 ^{\frac{2}{x}}})

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