derivative of (sec(x+csc(x))/(csc(x)))

Lösung

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

sec^{2} (x)

Schritte zur Lösung

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

Vereinfache

\frac{sec ( x ) + csc ( x )}{csc ( x )} : 1 + tan (x)

= \frac{d}{d x} (1 + tan (x))

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (1) + \frac{d}{d x} (tan (x))

\frac{d}{d x} (1) = 0

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

= 0 + sec^{2} (x)

Vereinfache

= sec^{2} (x)

\int cos (x) (tan (x) + sec (x)) d x

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

\frac{d}{d x} (25 - x^{2} - y^{2} - z^{2})

\frac{\partial}{\partial x} (x^{2} y e^{x - z})

in v erse l a pl a ce \frac{1}{1 + s} \cdot \frac{8}{s}