derivative of (2x/(sqrt(sec(x))))

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

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

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

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

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

= 2 \cdot \frac{1 \cdot sec ( x ) - \frac{t a n ( x ) s e c ( x )}{2} x}{( sec ( x ) ) ^{2}}

Vereinfache

2 \cdot \frac{1 \cdot sec ( x ) - \frac{t a n ( x ) s e c ( x )}{2} x}{( sec ( x ) ) ^{2}} : \frac{2 - x tan ( x )}{sec ( x )}

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

\int_{- 1}^{0.5} 1.5 x^{2} d x

\int \frac{x}{2 x ^{2} - 1} d x

\frac{d y}{d x} - (\frac{4}{x}) y = x^{5} e^{x}

x \to 6 - lim (c x^{2} + 3 x)

d er i v a t i v e \frac{x ^{2}}{1 + x ^{2}}