derivative of xe^xcot(x)

Lösung

\frac{d}{d x} (x e^{x} cot (x))

e^{x} cot (x) + x (e^{x} cot (x) - e^{x} csc^{2} (x))

Schritte zur Lösung

\frac{d}{d x} (x e^{x} cot (x))

Wende die Produktregel an:

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

f = x, g = e^{x} cot (x)

= \frac{d x}{d x} e^{x} cot (x) + \frac{d}{d x} (e^{x} cot (x)) x

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

\frac{d}{d x} (e^{x} cot (x)) = e^{x} cot (x) - e^{x} csc^{2} (x)

= 1 \cdot e^{x} cot (x) + (e^{x} cot (x) - e^{x} csc^{2} (x)) x

Vereinfache

= e^{x} cot (x) + x (e^{x} cot (x) - e^{x} csc^{2} (x))

\frac{d}{d x} (- 10 x + 3 cos (x))

\frac{d}{d x} (\frac{6 x}{x + 5})

\int e^{- 5 x} cos (3 x) d x

\frac{d}{d x} (\frac{1}{( x - 7 ) ^{2}})

d er i v a t i v e f (x) = tan (4) x^{3}