What is the derivative of arctan(sqrt(2t)) ?

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

What is the first derivative of arctan(sqrt(2t)) ?

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

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derivative of

arctan (2 t)

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

Solution steps

\frac{d}{d t} (arctan (2 t))

Simplify

arctan (2 t) : arctan (2 t)

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{- u ^{2} + 5}{( u ^{2} + 5 ) ^{2}}

\int ln (9 x + 7) d x

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

\int_{1}^{3} (3 x^{2} + 5 x - 4) d x

s - 1

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