derivative of 1/a sin(b+ax)

Lösung

\frac{d}{d x} (\frac{1}{a} sin (b + a x))

cos (b + a x)

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{a} sin (b + a x))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{a} \frac{d}{d x} (sin (b + a x))

Wende die Kettenregel an:

cos (b + a x) \frac{d}{d x} (b + a x)

= cos (b + a x) \frac{d}{d x} (b + a x)

\frac{d}{d x} (b + a x) = a

= \frac{1}{a} cos (b + a x) a

Vereinfache

\frac{1}{a} cos (b + a x) a : cos (b + a x)

= cos (b + a x)

\int e^{5 x} cos (x) d x

\frac{d}{d x} (\frac{8 x + 1}{x ^{- 5}})

\int x^{n + 2} d x

\int \frac{4 x ^{2} + 9 x + 4}{( x ^{2} + 1 ) ^{2}} d x

\int \frac{( 1 + x ) ^{2}}{x} d x