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Beliebt Rechnen >

derivative of (3x+2/(cos(x)))

Lösung

\frac{d}{d x} (\frac{3 x + 2}{cos ( x )})

Lösung

\frac{3 cos ( x ) + sin ( x ) ( 3 x + 2 )}{cos ^{2} ( x )}

Schritte zur Lösung

\frac{d}{d x} (\frac{3 x + 2}{cos ( x )})

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( 3 x + 2 ) cos ( x ) - \frac{d}{d x} ( cos ( x ) ) ( 3 x + 2 )}{( cos ( x ) ) ^{2}}

\frac{d}{d x} (3 x + 2) = 3

\frac{d}{d x} (cos (x)) = - sin (x)

= \frac{3 cos ( x ) - ( - sin ( x ) ) ( 3 x + 2 )}{( cos ( x ) ) ^{2}}

Vereinfache

= \frac{3 cos ( x ) + sin ( x ) ( 3 x + 2 )}{cos ^{2} ( x )}

Graph

Beliebte Beispiele

integral from 0 to 1 of (x^3)/(x^4-1)

\int_{0}^{1} \frac{x ^{3}}{x ^{4} - 1} d x

integral from 0 to 3 of (2t)/((t-4)^2)

\int_{0}^{3} \frac{2 t}{( t - 4 ) ^{2}} d t

inverselaplace 1/(s^2+9)

in v erse l a pl a ce \frac{1}{s ^{2} + 9}

integral of cos^2(x)sec^2(x)

\int cos^{2} (x) sec^{2} (x) d x

integral of xcos(x)-xsin(x)

\int x cos (x) - x sin (x) d x