What is the derivative of arctan(x^{1/2}) ?

The derivative of arctan(x^{1/2}) is 1/(2x^{1/2)(x+1)}

What is the first derivative of arctan(x^{1/2}) ?

The first derivative of arctan(x^{1/2}) is 1/(2x^{1/2)(x+1)}

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int (x + 3) (x^{2} + 6 x - 7) d x

\frac{\partial}{\partial x} (x^{2} + z^{2})

\frac{1}{x ^{2} ( x ^{2} + 4 x + 13 )}

\int_{0}^{2} 3 x d x

\int (3 u + \frac{1}{u}) d u

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