derivative of sin({p}(x)ix)

Lösung

\frac{d}{d x} (sin (p (x)) i x)

i (sin (p (x)) + x cos (p (x)) \frac{d}{d x} (p (x)))

Schritte zur Lösung

\frac{d}{d x} (sin (p (x)) i x)

Entferne die Konstante:

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

= i \frac{d}{d x} (sin (p (x)) x)

Wende die Produktregel an:

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

f = sin (p (x)), g = x

= i (\frac{d}{d x} (sin (p (x))) x + \frac{d x}{d x} sin (p (x)))

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

\frac{d x}{d x} = 1

= i (cos (p (x)) \frac{d}{d x} (p (x)) x + 1 \cdot sin (p (x)))

Vereinfache

i (cos (p (x)) \frac{d}{d x} (p (x)) x + 1 \cdot sin (p (x))) : i (sin (p (x)) + x cos (p (x)) \frac{d}{d x} (p (x)))

= i (sin (p (x)) + x cos (p (x)) \frac{d}{d x} (p (x)))

d er i v a t i v e cos (8 x)

in v erse l a pl a ce \frac{s}{( s - 3 ) ^{2}}

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