What is the derivative of arctan(sqrt(3t)) ?

The derivative of arctan(sqrt(3t)) is (sqrt(3))/(2sqrt(t)(3t+1))

What is the first derivative of arctan(sqrt(3t)) ?

The first derivative of arctan(sqrt(3t)) is (sqrt(3))/(2sqrt(t)(3t+1))

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derivative of

arctan (3 t)

\frac{3}{2 t ( 3 t + 1 )}

Solution steps

\frac{d}{d t} (arctan (3 t))

Simplify

arctan (3 t) : arctan (3 t)

= \frac{d}{d t} (arctan (3 t))

Apply the chain rule:

\frac{1}{( 3 t ) ^{2} + 1} \frac{d}{d t} (3 t)

= \frac{1}{( 3 t ) ^{2} + 1} \frac{d}{d t} (3 t)

\frac{d}{d t} (3 t) = \frac{3}{2 t}

= \frac{1}{( 3 t ) ^{2} + 1} \cdot \frac{3}{2 t}

Simplify

\frac{1}{( 3 t ) ^{2} + 1} \cdot \frac{3}{2 t} : \frac{3}{2 t ( 3 t + 1 )}

= \frac{3}{2 t ( 3 t + 1 )}

y^{^{''}} + 2 y^{^{'}} + 17 y = 0, y (0) = 3, y^{^{'}} (0) = - 2

\int e^{- 4 x} sin (b x) d x

\int_{5}^{3} 2 d x

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

\int 2 cot^{3} (x) csc^{3} (x) d x

What is the derivative of arctan(sqrt(3t)) ?
The derivative of arctan(sqrt(3t)) is (sqrt(3))/(2sqrt(t)(3t+1))
What is the first derivative of arctan(sqrt(3t)) ?
The first derivative of arctan(sqrt(3t)) is (sqrt(3))/(2sqrt(t)(3t+1))