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

The derivative of 1/2 arctan((x+1/2)) is 1/(x^2+2x+5)

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

The first derivative of 1/2 arctan((x+1/2)) is 1/(x^2+2x+5)

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

\frac{1}{x ^{2} + 2 x + 5}

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2} \cdot \frac{1}{( \frac{x + 1}{2} ) ^{2} + 1} \cdot \frac{1}{2} : \frac{1}{x ^{2} + 2 x + 5}

= \frac{1}{x ^{2} + 2 x + 5}

\int sec (t) (sec (t) + tan (t)) d t

\int v^{- \frac{7}{8}} d v

y = 3 x - x^{2}, y = 0

\int \frac{3}{x ^{2} + x + 1} d x

\frac{d}{d x} ((x^{2} - x)^{2} - 2 (x^{2} - x))

What is the derivative of 1/2 arctan((x+1/2)) ?
The derivative of 1/2 arctan((x+1/2)) is 1/(x^2+2x+5)
What is the first derivative of 1/2 arctan((x+1/2)) ?
The first derivative of 1/2 arctan((x+1/2)) is 1/(x^2+2x+5)