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Popular >

derivative of f(x)=arctan(sqrt(x))

Solution

derivative of

f (x) = arctan (x)

Solution

\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 )}

Popular Examples

(\partial)/(\partial x)((xy)^{xy})

\frac{\partial}{\partial x} ((x y)^{x y})

integral of 3-tan(x/6)

\int 3 - tan (\frac{x}{6}) d x

(\partial)/(\partial y)(xye^y)

\frac{\partial}{\partial y} (x y e^{y})

integral of (8x^2+x+8)/((x^2+1)^2)

\int \frac{8 x ^{2} + x + 8}{( x ^{2} + 1 ) ^{2}} d x

tangent of f(x)=2e^x,\at x=2 tangent of

f (x) = 2 e^{x}, at x = 2

Frequently Asked Questions (FAQ)

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))