What is the derivative of arctan(tan(x)) ?

The derivative of arctan(tan(x)) is 1

What is the first derivative of arctan(tan(x)) ?

The first derivative of arctan(tan(x)) is 1

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\frac{d}{d x} (arctan (tan (x)))

1

Solution steps

\frac{d}{d x} (arctan (tan (x)))

Apply the chain rule:

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

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

\frac{d}{d x} (tan (x)) = sec^{2} (x)

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

Simplify

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

= 1

x \to 0 + lim (x ln (x^{2}))

y = 9 - x^{2}, y = 0, x

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

\frac{\partial}{\partial x} (4 + x ln (x y - 5))

\frac{d}{d x} (x (2 - x))

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