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

Lösung

\frac{d}{d x} (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 e^{x} \cdot \frac{1}{2 x} d x

\frac{d}{d x} (\frac{x ^{2} + x - 2}{2 x ^{2} - 2})

f (x) = x^{5 x}

\int u^{- 3} (4 - u^{3} + u^{6}) d u

d er i v a t i v e e^{x} (x^{3} - 3 x^{2} + 6 x - 6)