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Popular >

derivative of sqrt(arctan(x))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

integral from 1 to 6 of (x^2+8)/(7x-x^2)

\int_{1}^{6} \frac{x ^{2} + 8}{7 x - x ^{2}} d x

tangent of f(x)=-2x^3,(2,-16)tangent of

f (x) = - 2 x^{3}, (2, - 16)

(dy)/(dx)=(x+y+7)^2

\frac{d y}{d x} = (x + y + 7)^{2}

integral from-r to r of sqrt(r^2-x^2)

\int_{- r}^{r} r^{2} - x^{2} d x

derivative of 8/(1+8x)

\frac{d}{d x} (\frac{8}{1 + 8 x})

Frequently Asked Questions (FAQ)

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