derivative of 7sin(xe^{-x}-1)

Lösung

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

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (7 sin (x) e^{- x}) - \frac{d}{d x} (1)

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

\frac{d}{d x} (1) = 0

= 7 (e^{- x} cos (x) - e^{- x} sin (x)) - 0

Vereinfache

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

\frac{\partial}{\partial x} (e^{2 x} - x cos (x y))

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

\int \frac{1}{x ^{3} - x} d x

2 y^{^{''}} + y^{^{'}} + 3 y = 3 cos (3 t) + 2 sin (3 t)

\int_{0}^{2} π (2 x - x^{2})^{2} d x