derivative of (sin(x+cos(x))sec(x))

Lösung

\frac{d}{d x} ((sin (x) + cos (x)) sec (x))

sec^{2} (x)

Schritte zur Lösung

\frac{d}{d x} ((sin (x) + cos (x)) sec (x))

Vereinfache

(sin (x) + cos (x)) sec (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)

t an g e n t f (x) = 5 x + 4, at x = 1

\frac{d}{d x} (arctan (x) + arccos (x))

x \to \infty lim (4 x + 5)

t an g e n t f (x) = \frac{2}{x}, at x = 2

n = 1 \sum \infty (\frac{2}{n})^{n} \cdot n!