derivative of sqrt(sin(7x+ln(5x)))

Lösung

\frac{d}{d x} (sin (7 x + ln (5 x)))

\frac{cos ( 7 x + ln ( 5 x ) ) ( 7 x + 1 )}{2 x sin ( 7 x + ln ( 5 x ) )}

Schritte zur Lösung

\frac{d}{d x} (sin (7 x + ln (5 x)))

Wende die Kettenregel an:

\frac{1}{2 sin ( 7 x + ln ( 5 x ) )} \frac{d}{d x} (sin (7 x + ln (5 x)))

= \frac{1}{2 sin ( 7 x + ln ( 5 x ) )} \frac{d}{d x} (sin (7 x + ln (5 x)))

\frac{d}{d x} (sin (7 x + ln (5 x))) = cos (7 x + ln (5 x)) (7 + \frac{1}{x})

= \frac{1}{2 sin ( 7 x + ln ( 5 x ) )} cos (7 x + ln (5 x)) (7 + \frac{1}{x})

Vereinfache

\frac{1}{2 sin ( 7 x + ln ( 5 x ) )} cos (7 x + ln (5 x)) (7 + \frac{1}{x}) : \frac{cos ( 7 x + ln ( 5 x ) ) ( 7 x + 1 )}{2 x sin ( 7 x + ln ( 5 x ) )}

= \frac{cos ( 7 x + ln ( 5 x ) ) ( 7 x + 1 )}{2 x sin ( 7 x + ln ( 5 x ) )}

x \to 0 lim (\frac{1}{x ^{2} ( x + 7 )})

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\int \frac{1}{9 x - 4} d x

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