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Popular >

derivative of arctan(sqrt(3x))

Solution

derivative of

arctan (3 x)

Solution

\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 )}

Popular Examples

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\int \frac{( 36 - 25 x ^{2} ) ^{\frac{3}{2}}}{x ^{6}} d x

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limit as x approaches 3 of (8)+6(-7)

x \to 3 lim ((8) + 6 (- 7))

Frequently Asked Questions (FAQ)

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))