derivative of arctan(tan(x))

Lösung

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

1

Schritte zur Lösung

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

Wende die Kettenregel an:

\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)

Vereinfache

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

= 1

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

a re a 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))