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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

d er i v a t i v e x^{c o s (x)}

- 5 t^{2} y^{^{''}} + t y^{^{'}} + 8 y = 0

a re a \frac{3}{x}, 12 x, \frac{1}{3} x

\int r 1 + 4 r^{2} d r

t an g e n t f (x) = cos (x), at x = \frac{π}{4}