derivative of e^xsin(x+cos(x)e^x)

Lösung

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

2 e^{x} cos (x)

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Vereinfache

= 2 e^{x} cos (x)

\frac{d}{d x} (\frac{- 6 x}{( x ^{2} - 4 ) ^{2}})

\int e^{x^{0.5}} d x

\frac{\partial}{\partial x} (a x^{b} y^{(1 - b)})

\frac{d y}{d x} = (- 10 x^{4} y)

\frac{d}{d x} (\frac{1}{6} x^{3})