derivative of 31arctan(sqrt(x))

Lösung

\frac{d}{d x} (31 arctan (x))

\frac{31}{2 x ( x + 1 )}

Schritte zur Lösung

\frac{d}{d x} (31 arctan (x))

Entferne die Konstante:

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

= 31 \frac{d}{d x} (arctan (x))

Wende die Kettenregel an:

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

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

\frac{d}{d x} (x) = \frac{1}{2 x}

= 31 \cdot \frac{1}{( x ) ^{2} + 1} \cdot \frac{1}{2 x}

Vereinfache

31 \cdot \frac{1}{( x ) ^{2} + 1} \cdot \frac{1}{2 x} : \frac{31}{2 x ( x + 1 )}

= \frac{31}{2 x ( x + 1 )}

\frac{\partial}{\partial x} (e^{y} + x + x^{2} + 4)

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