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

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

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

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

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

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

Solution steps

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

Simplify

arctan (3 x) : arctan (3 x)

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{s - 3}{4 s ^{2} + s + 12}

\int_{0}^{25} (- 12 x) d x

(- 5, - 8), (- 1, 4)

x \to 2 lim (x + 2 + \frac{4}{x})

x \to \infty lim (x (x^{2} + 4 - x))

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