derivative of e^xsin(e^x)

Lösung

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

e^{x} sin (e^{x}) + e^{2 x} cos (e^{x})

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

\frac{d}{d x} (sin (e^{x})) = cos (e^{x}) e^{x}

= e^{x} sin (e^{x}) + cos (e^{x}) e^{x} e^{x}

cos (e^{x}) e^{x} e^{x} = e^{2 x} cos (e^{x})

= e^{x} sin (e^{x}) + e^{2 x} cos (e^{x})

\frac{d}{d t} (e^{3 c o s (t) + 2 t^{2}})

\int sec^{2} (2 x y) d x

\frac{d}{d x} (\frac{x ^{2} - 8 x + 7}{x ^{2} + 9})

\frac{\partial}{\partial x} (t^{2} e^{x} + 3 x^{2})

x \to 2 lim (x^{2} + x - 6)