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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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