What is the (arctan(sqrt(x)))^' ?

The (arctan(sqrt(x)))^' is 1/(2sqrt(x)(x+1))

What is the first (arctan(sqrt(x)))^' ?

The first (arctan(sqrt(x)))^' is 1/(2sqrt(x)(x+1))

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(arctan (x))^{^{'}}

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

Solution steps

(arctan (x))^{'}

Apply the chain rule:

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

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

\frac{d}{d x} (8 e^{x} + \frac{8}{3 x})

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

\int \frac{4}{( x + 1 ) ( x + 3 )} d x

x \to \infty lim (\frac{8 ^{x}}{9 ^{x + 1}})

\int \frac{32}{1 - cos ( 4 x )} d x

What is the (arctan(sqrt(x)))^' ?
The (arctan(sqrt(x)))^' is 1/(2sqrt(x)(x+1))
What is the first (arctan(sqrt(x)))^' ?
The first (arctan(sqrt(x)))^' is 1/(2sqrt(x)(x+1))