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Popular >

derivative of ln(arctan(x+1))

Solution

derivative of

ln (arctan (x + 1))

Solution

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

Solution steps

\frac{d}{d x} (ln (arctan (x + 1)))

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

(\partial)/(\partial t)((rs)/(s^2+t^2))

\frac{\partial}{\partial t} (\frac{rs}{s ^{2} + t ^{2}})

derivative of (8x^2+3(3-x^2+7x))

\frac{d}{d x} ((8 x^{2} + 3) (3 - x^{2} + 7 x))

inverse oflaplace (e^{-s})/(s-2)inverse laplace

\frac{e ^{- s}}{s - 2}

derivative of 1/(x^2ln(x))

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

tangent of f(x)=sqrt(7x+11),\at x=2 tangent of

f (x) = 7 x + 11, at x = 2

Frequently Asked Questions (FAQ)

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