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Beliebt Rechnen >

derivative of e^{4x^2}csc(5x)

Lösung

\frac{d}{d x} (e^{4 x^{2}} csc (5 x))

Lösung

8 e^{4 x^{2}} x csc (5 x) - 5 e^{4 x^{2}} cot (5 x) csc (5 x)

Schritte zur Lösung

\frac{d}{d x} (e^{4 x^{2}} csc (5 x))

Wende die Produktregel an:

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

f = e^{4 x^{2}}, g = csc (5 x)

= \frac{d}{d x} (e^{4 x^{2}}) csc (5 x) + \frac{d}{d x} (csc (5 x)) e^{4 x^{2}}

\frac{d}{d x} (e^{4 x^{2}}) = e^{4 x^{2}} \cdot 8 x

\frac{d}{d x} (csc (5 x)) = - cot (5 x) csc (5 x) \cdot 5

= e^{4 x^{2}} \cdot 8 x csc (5 x) + (- cot (5 x) csc (5 x) \cdot 5) e^{4 x^{2}}

Vereinfache

= 8 e^{4 x^{2}} x csc (5 x) - 5 e^{4 x^{2}} cot (5 x) csc (5 x)

Graph

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