derivative of ln(xsec(x))

Lösung

\frac{d}{d x} (ln (x) sec (x))

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

Schritte zur Lösung

\frac{d}{d x} (ln (x) sec (x))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = ln (x), g = sec (x)

= \frac{d}{d x} (ln (x)) sec (x) + \frac{d}{d x} (sec (x)) ln (x)

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

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

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

\frac{1}{x} sec (x) = \frac{sec ( x )}{x}

= \frac{sec ( x )}{x} + sec (x) tan (x) ln (x)

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