derivative of k(sec(x+tan(x)))

Lösung

\frac{d}{d x} (k (sec (x) + tan (x)))

- \frac{k}{- 1 + sin ( x )}

Schritte zur Lösung

\frac{d}{d x} (k (sec (x) + tan (x)))

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

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

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

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

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

= k (sec (x) tan (x) + sec^{2} (x))

Vereinfache

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

= - \frac{k}{- 1 + sin ( x )}

\int (1 + \frac{9}{4} x)^{\frac{1}{2}} d x

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

d er i v a t i v e 3 cos (x) + 2 sin (x)

(\frac{x}{3})^{^{'}}

y - x \frac{d y}{d x} = 0