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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int_{2}^{3} 2 x d x

\frac{7}{4} x^{4} - \frac{6}{5} x^{3}

x \to 0 lim (\frac{e ^{x} - 1}{17 x})

f (x) = 3^{x} - 5 e^{x}

\frac{d}{d x} (x^{3} - 7)

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