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Popular >

derivative of 2arctan(sqrt(x))

Solution

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

Solution

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \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}

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

Simplify

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

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

Popular Examples

(\partial}{\partial x}(\frac{x^2)/2+(y^3)/3)

\frac{\partial}{\partial x} (\frac{x ^{2}}{2} + \frac{y ^{3}}{3})

derivative of f(x)=5ex derivative of

f (x) = 5 e x

d/(dt)(t^{1/2})

\frac{d}{d t} (t^{\frac{1}{2}})

limit as x approaches 0 of ((3+x^2)-9)/x

x \to 0 lim (\frac{( 3 + x ^{2} ) - 9}{x})

derivative of (2x^2+x+9^{-3})

\frac{d}{d x} ((2 x^{2} + x + 9)^{- 3})

Frequently Asked Questions (FAQ)

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