derivative ln(sec(5x)+tan(5x))

Lösung

ableitung von

ln (sec (5 x) + tan (5 x))

5 sec (5 x)

Schritte zur Lösung

\frac{d}{d x} (ln (sec (5 x) + tan (5 x)))

Wende die Kettenregel an:

\frac{1}{sec ( 5 x ) + tan ( 5 x )} \frac{d}{d x} (sec (5 x) + tan (5 x))

= \frac{1}{sec ( 5 x ) + tan ( 5 x )} \frac{d}{d x} (sec (5 x) + tan (5 x))

\frac{d}{d x} (sec (5 x) + tan (5 x)) = sec (5 x) tan (5 x) \cdot 5 + sec^{2} (5 x) \cdot 5

= \frac{1}{sec ( 5 x ) + tan ( 5 x )} (sec (5 x) tan (5 x) \cdot 5 + sec^{2} (5 x) \cdot 5)

Vereinfache

\frac{1}{sec ( 5 x ) + tan ( 5 x )} (sec (5 x) tan (5 x) \cdot 5 + sec^{2} (5 x) \cdot 5) : 5 sec (5 x)

= 5 sec (5 x)

\int 5 \frac{cos ( x ) + sin ( 2 x )}{sin ( x )} d x

n = 1 \sum \infty 8 (- \frac{1}{4})^{n}

x \to 0 + lim (2 x ln (x))

x^{2} + 4, - x^{2} - 1, x = - 2, x = 3

f (x) = x^{2} ln (2 x)