What is the derivative of arctan(x-5) ?

The derivative of arctan(x-5) is 1/(x^2-10x+26)

What is the first derivative of arctan(x-5) ?

The first derivative of arctan(x-5) is 1/(x^2-10x+26)

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\frac{d}{d x} (arctan (x - 5))

\frac{1}{x ^{2} - 10 x + 26}

Solution steps

\frac{d}{d x} (arctan (x - 5))

Apply the chain rule:

\frac{1}{( x - 5 ) ^{2} + 1} \frac{d}{d x} (x - 5)

= \frac{1}{( x - 5 ) ^{2} + 1} \frac{d}{d x} (x - 5)

\frac{d}{d x} (x - 5) = 1

= \frac{1}{( x - 5 ) ^{2} + 1} \cdot 1

Simplify

\frac{1}{( x - 5 ) ^{2} + 1} \cdot 1 : \frac{1}{x ^{2} - 10 x + 26}

= \frac{1}{x ^{2} - 10 x + 26}

What is the derivative of arctan(x-5) ?
The derivative of arctan(x-5) is 1/(x^2-10x+26)
What is the first derivative of arctan(x-5) ?
The first derivative of arctan(x-5) is 1/(x^2-10x+26)