What is the derivative of arctan(sqrt(t)) ?

The derivative of arctan(sqrt(t)) is 1/(2sqrt(t)(t+1))

What is the first derivative of arctan(sqrt(t)) ?

The first derivative of arctan(sqrt(t)) is 1/(2sqrt(t)(t+1))

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derivative of

arctan (t)

\frac{1}{2 t ( t + 1 )}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{1}{2 t ( t + 1 )}

\int (16 x + 7) d x

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\frac{d}{d x} (ln (\frac{3 x + 4}{3 x - 4}))

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