derivative of 7(e^xcos(x-e^xsin(x)))

Lösung

\frac{d}{d x} (7 (e^{x} cos (x) - e^{x} sin (x)))

- 14 e^{x} sin (x)

Schritte zur Lösung

\frac{d}{d x} (7 (e^{x} cos (x) - e^{x} sin (x)))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 7 \frac{d}{d x} (e^{x} cos (x) - e^{x} sin (x))

Wende die Summen-/Differenzregel an:

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

= 7 (\frac{d}{d x} (e^{x} cos (x)) - \frac{d}{d x} (e^{x} sin (x)))

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

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

= 7 (e^{x} cos (x) - e^{x} sin (x) - (e^{x} sin (x) + cos (x) e^{x}))

Vereinfache

7 (e^{x} cos (x) - e^{x} sin (x) - (e^{x} sin (x) + cos (x) e^{x})) : - 14 e^{x} sin (x)

= - 14 e^{x} sin (x)

d er i v a t i v e 3 (x^{2} - 1)^{2}

\frac{d y}{d x} = \frac{3 x}{5 y}

\frac{\partial}{\partial x} (y^{x z} + 2 (yz)^{x})

\int 2 4 x d x

\int \frac{tan ( ln ( y ) )}{y} d y