derivative of 6arcsinh(tan(x))

Lösung

\frac{d}{d x} (6 arcsinh (tan (x)))

6 sec (x)

Schritte zur Lösung

\frac{d}{d x} (6 arcsinh (tan (x)))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 6 \frac{d}{d x} (arcsinh (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)

= 6 \cdot \frac{1}{( tan ( x ) ) ^{2} + 1} sec^{2} (x)

Vereinfache

6 \cdot \frac{1}{tan ^{2} ( x ) + 1} sec^{2} (x) : 6 sec (x)

= 6 sec (x)

\frac{\partial}{\partial x} (ln (6 x^{2} - 4 y^{2}))

x \to 7 lim (\frac{9 x}{x - 7})

\frac{d y}{d x} = e^{- x} - y

d er i v a t i v e y = x^{\frac{17}{18}}

\frac{\partial}{\partial y} (y \cdot ln (x))