derivative of (5tan(x)/x)

Lösung

\frac{d}{d x} (\frac{5 tan ( x )}{x})

\frac{5 ( x sec ^{2} ( x ) - tan ( x ) )}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{5 tan ( x )}{x})

Entferne die Konstante:

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

= 5 \frac{d}{d x} (\frac{tan ( x )}{x})

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= 5 \cdot \frac{\frac{d}{d x} ( tan ( x ) ) x - \frac{d x}{d x} tan ( x )}{x ^{2}}

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

\frac{d x}{d x} = 1

= 5 \cdot \frac{sec ^{2} ( x ) x - 1 \cdot tan ( x )}{x ^{2}}

Vereinfache

5 \cdot \frac{sec ^{2} ( x ) x - 1 \cdot tan ( x )}{x ^{2}} : \frac{5 ( x sec ^{2} ( x ) - tan ( x ) )}{x ^{2}}

= \frac{5 ( x sec ^{2} ( x ) - tan ( x ) )}{x ^{2}}

\int \frac{7}{5 y - 105} d y

\frac{\partial}{\partial x} (x^{2} + x y - 25)

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

\int t^{2} - 4 d t

\frac{d}{d x} (x + x^{3})