What is the derivative of arctan(x-1) ?

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

What is the first derivative of arctan(x-1) ?

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

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\frac{d}{d x} (arctan (x - 1))

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

Solution steps

\frac{d}{d x} (arctan (x - 1))

Apply the chain rule:

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

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

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

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

Simplify

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

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

y^{^{'}} - (\frac{2 x}{( 1 + x ^{2} )}) y = 0

\int ln (e^{u^{2}}) d u

3 x - 4 y x^{2} + 1 \frac{d y}{d x} = 0

x \to 3 lim (x^{2} - 4 x)

\int \frac{4}{4 x - 1} d x

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