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Beliebt Rechnen >

(f(x)e^{g(x)})'

Lösung

(f (x) e^{g (x)})^{'}

Lösung

f' (x) e^{g (x)} + e^{g (x)} g' (x) f (x)

Schritte zur Lösung

(f (x) e^{g (x)})^{'}

Wende die Produktregel an:

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

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

= f^{^{'}} (x) e^{g (x)} + (e^{g (x)})^{^{'}} f (x)

(e^{g (x)})^{'} = e^{g (x)} g^{'} (x)

= f^{^{'}} (x) e^{g (x)} + e^{g (x)} g^{^{'}} (x) f (x)

Beliebte Beispiele

derivative of sqrt(x)-x

\frac{d}{d x} (x - x)

(d^3)/(dx^3)(e^{2x})

\frac{d ^{3}}{d x ^{3}} (e^{2 x})

limit as x approaches 0 of (1-x)/(x^2)

x \to 0 lim (\frac{1 - x}{x ^{2}})

y^{^{''}} + 4 y = 20

integral of 5x-sqrt(x)

\int 5 x - x d x